Skip to main content Accessibility help
×
  • Cited by 146
Publisher:
Cambridge University Press
Online publication date:
August 2014
Print publication year:
2000
Online ISBN:
9780511805141

Book description

This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.

Reviews

‘I welcome the paperback edition version of this masterfully written text.’

Paul Embrechts Source: JASA

‘The monograph as a whole is warmly recommended to post-PhD students of probability and will be welcomed as a good and reliable reference.’

Source: EMS

‘… will be read with pleasure and advantage by experts in the field and its applications, as well as by those probabilists and others who wish to learn the subject … an exciting and enjoyable introduction to the rich ideas of the Itô calculus … there is nothing dry about this book, for its authors have already breathed life into a vibrant subject.’

Mathematics Today

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
×

Contents

References
[1] Abrahams, R. and Robbin, J.Transversal Mappings and Flows, Benjamin, New York, Amsterdam, 1967.
[1] Aizenmann, M. and Simon, B.Brownian motion and the Harnack inequality for Schrödinger operators, Comm. Pure and Appl. Math., 35, 209-273 (1982).
[1] Albeverio, S., Blanchard, Ph. and Høegh-Krohn, R.Newtonian diffusions and planets, with a remark on non-standard Dirichlet forms and polymers, Stochastic Analysis and Applications: Lecture Notes in Mathematics 1095, Springer, Berlin, 1984, pp. 1–24.
[1] Albeverio, S., Fenstad, I. E., Hoegh-Krohn, R. and Lindström, T.Non-standard Methods in Probability and Mathematical Physics.
[1] Aldous, D.Stopping times and tightness, Ann. Prob., 6, 335–40 1978.
[1] Ancona, A.Negatively curved manifolds, elliptic operators and Martin boundary (to appear).
[1] Arnold, L. and Wihstutz, V. (editors) Lyapunov Exponents (Proceedings): Lecture Notes in Mathematics 1186, Springer, Berlin, 1986.
[1] Azema, J. and Yor, M.Une solution simple au problème de Skorokhod, Séminaire de Probabilités XIII: Lecture Notes in Mathematics 721, Springer, Berlin, 1979, pp. 90–115, 625–633.
[2] Azema, J. and Yor, M. (Editors) Temps locaux, Astérisque52-53, Société Mathématique de France, 1978.
[1] Azencott, Grandes déviations et applications, Ecole d'Été de Probabilités de Saint-Flour VIII: Lecture Notes in Mathematics 774, Springer, Berlin, 1980.
[1] Barlow, M. T.Study of a filtration expanded to include an honest time, Z. Wahrscheinlichkeitstheorie, 44, 307–323 1978.
[2] Barlow, M. T.Decomposition of a Markov process at an honest time (unpublished).
[3] Barlow, M. T.One dimensional stochastic differential equation with no strong solution, J. London Math. Soc, 26, 335–347 1982.
[4] Barlow, M. T.On Brownian local time, Séminaire de Probabilités X V: Lecture Notes in Mathematics 850, Springer, Berlin, 1981, pp. 189–190.
[1] Barlow, M. T., Jacka, S. and Yor, M.Inequalities for a pair of processes stopped at a random time, Proc. London Math. Soc, 52, 142–172 1986.
[2] Barlow, M. T., Jacka, S. and Yor, M.Inégalities pour un couple de processus arrêtés à un temps quelconque, C. R. Acad. Sci., 299, 351–354 1984.
[1] Barlow, M. T. And Perkins, E.One-dimensional stochastic differential equations involving a singular increasing process, Stochastics, 12, 229–249 1984.
[2] Barlow, M. T. And Perkins, E.Strong existence, uniqueness and non-uniqueness in an equation involving local time, Séminaire de Probabilités X VII: Lecture Notes in Mathematics 986, Springer, Berlin, 1983, pp. 32–66.
[1] Barlow, M. T. and Yor, M.(Semi-) martingale inequalities and local times, Z. Wahrscheinlichkeitstheorie, 55, 237–254 1981.
[2] Barlow, M. T. and Yor, M.Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma and applications to local times, J. Funct. Anal., 49, 198–229 1982.
[1] Bass, R. and Cranston, M.The Malliavin calculus for pure jump processes and applications to local time, Ann. Prob., 14, 490–532 1986.
[1] Baxendale, P.Asymptotic behaviour of stochastic flows of diffeomorphisms; two case studies, Probab. Th. Rel. Fields, 73, 51–85 1986.
[2] Baxendale, P.Moment stability and large deviations for linear stochastic differential equations,
[3] Baxendale, P.The Lyapunov spectrum of a stochastic flow of diffeomorphisms.
[4] Baxendale, P.Brownian motions on the diffeomorphism group, I, Compos. Math., 53, 19-50 (1984).
[1] Baxendale, P. and Stroock, D. W.Paper on Lyapunov exponents (to appear).
[1] Bensoussan, A.Lectures on stochastic control, Nonlinear Filtering and Stochastic Control: Lecture Notes in Mathematics 972, Springer, Berlin, 1982, pp. 1–62.
[1] Benes, V. E., Shepp, L. A. and Witsenhausen, H. S.Some solvable stochastic control problems, Stochastics, 4, 39–83 1980.
[1] Benveniste, A. and Jacod, J.Systèmes de Lévy des processus de Markov, Invent. Math., 21, 183–198 1973.
[1] Berman, S. M.Local times and sample function properties of stationary Gaussian processes, Trans. Amer. Math. Soc, 137, 277–300 1969.
[2] Berman, S. M.Harmonic analysis of local times and sample functions of Gaussian processes, Trans. Amer. Math. Soc, 143, 269–281 1969.
[3] Berman, S. M.Gaussian processes with stationary increments: local times and sample function properties, Ann. Math. Statist., 41, 1260–1272 1970.
[1] Bichteler, K.Stochastic integration and ZAtheory of semi-martingales, Ann. Prob., 9, 49-89 (1981).
[1] Bichteler, K. and Fonken, D.A simple version of the Malliavin calculus in dimension one, Martingale Theory in Harmonic Analysis and Banach Spaces: Lecture Notes in Mathematics 939, Springer, Berlin, 1982, pp. 6–12.
[1] Bichteler, K. and Jacod, J.Calcul de Malliavin pour les diffusions avec sauts: Existence d'une densité dans le cas unidimensionnel, Séminaire de Probabilités X VII: Lecture Notes in Mathematics 986, Springer, Berlin, 1983, pp. 132–157.
[1] Blllingsley, P.Ergodic Theory and Information, Wiley, New York, 1965.
[2] Blllingsley, P.Convergence of Probability Measures, Wiley, New York, 1968.
[3] Blllingsley, P.Conditional distributions and tightness, Ann. Prob., 2, 480–485 1974.
[1] Bingham, N. H. and Doney, R. A.On fluctuation theory in higher dimensions.
[1] Bishop, R. and Crittenden, R. J.Geometry of Manifolds, Academic Press, New York, 1964.
[1] Bismut, J.-M.Méchanique Aléatoire: Lecture Notes in Mathematics 866, Springer, Berlin, 1981.
[2] Bismut, J.-M.Martingales, the Malliavin calculus and hypoellipticity under general Hormander's conditions, Z. Wahrscheinlichkeitstheorie, 56, 469–505 1981.
[3] Bismut, J.-M.Calcul de variations stochastiques et processus de sauts Z. Wahrscheinlichkeitstheorie, 56, 469–505 1983.
[4] Bismut, J.-M.Large deviations and the Malliavin calculus, Progress in Math., Birkhauser, Boston, 1984.
[5] Bismut, J.-M.The Atiyah-Singer theorems; a probabilistic approach: I, The index theorem, J. Fund. Anal, 57, 56-98 (1984); II, The Lefschetz fixed-point formulas, J. Fund. Anal, 329-348.
[1] Bismut, J.-M. and Michel, D.Diffusions conditionnelles, I, II, J. Funct. Anal., 44, 174-211 (1981); 45,274-292(1981).
[1] Blackwell, D. and Kendall, D. G.The Martin boundary for Polya's urn scheme and an application to stochastic population growth, J. Appl. Prob., 1, 284–296 1964.
[1] Blumenthal, R. M. and Getoor, R. K.Markov Processes and Potential Theory, Academic Press, New York, 1968.
[1] Breiman, L.Probability, Addison-Wesley, Reading, Mass., 1968.
[1] Bremaud, P.Point Processes and Queues: Martingale Dynamics, Springer, New York, 1981.
[1] Bourbaki, N.Topologie générale, in Eléments de Mathématique, Hermann, Paris, 1958, Chap. IX, 2nd edition.
[1] Bougerol, P. and Lacroix, J.Products of Random Matrices with Applications to Schrbdinger Operators, Birkhauser, Boston, 1985.
[1] Burkholder, D.Distribution function inequalities for martingales, Ann. Prob., 1, 19–42 1973.
[1] Carlen, E. A.Conservative diffusions, Comm. Math. Phys., 94, 293–315 1984.
[2] Carlen, E. A.Potential scattering in quantum mechanics, Ann. Inst. H. Poincaré, 42, 407-428 (1985).
[1] Carverhill, A. P.Flows of stochastic dynamical systems: ergodic theory, Stochastics, 14, 273–318 1985.
[2] Carverhill, A. P.A formula for the Lyapunov exponents of a stochastic flow. Application to a perturbation theorem, Stochastics, 14, 209–226 1985.
[3] Carverhill, A. P.A ‘Markovian’ approach to the multiplicative ergodic (Oseledec) theorem for nonlinear stochastic dynamical systems.
[1] Carverhill, A. P., Chappell, M. J. and Elworthy, K. D.Characteristic exponents for stochastic flows, Proceedings, BIBOS I: Stochastic Processes.
[1] Carverhill, A. P. and Elworthy, K. D.Flows of stochastic dynamical systems; the functional analytic approach, Z. Wahrscheinlichkeitstheorie, 65, 245–268 1983.
[1] Chaleyat-Maurel, MireilleLa condition d'hypoellipticité d'Hörmander, Astérisque, 84–85, 189-202 (1981).
[1] Chaleyat-Maurel, Mireille and El Karoui, NicoleUn problème de réflexion et ses applications au temps local et aux équations différentielles stochastiques sur M, cas continu. In Azema and Yor [2], pp. 117–144.
[1] Cheeoer, J. and Ebin, D. G.Comparison Theorems in Riemannian Geometry, North-Holland, Amsterdam, Oxford, New York, 1975.
[1] Chung, K. L.Markov Chains with Stationary Transition Probabilities, 2nd edition, Springer, Berlin, 1967.
[2] Chung, K. L.Probabilistic approach in potential theory to the equilibrium problem, Ann. Inst. Fourier, Grenoble, 23, 313–322 1973.
[3] Chung, K. L.Excursions in Brownian motion, Ark. Mat., 14, 155–177 1976.
[1] Chung, K. L. and Getoor, R. K.The condenser problem, Ann. Prob., 5, 82–86 1977.
[1] Chung, K. L. and Walsh, J. B.To reverse a Markov process, Acta Math., 123, 225–251 1969.
[2] Chung, K. L. and Walsh, J. B.Meyer's theorem on previsibility, Z. Wahrscheinlichkeitstheorie, 29, 253–256 1974.
[1] Chung, K. L. and Williams, R. J.Introduction to Stochastic Integration, Birkhauser, Boston, 1983.
[1] Ciesielski, Z. and Taylor, S. J.First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path, Trans. Am. Math. Soc, 103, 434–450 1962.
[1] Çinlar, E., Jacod, J., Protter, P. and Sharpe, M. J.Semimartingales and Markov processes, Z. Wahrscheinlichkeitstheorie, 54, 161–220 1980.
[1] Çinlar, E., Chung, K. L. and Getoor, R. K. (editors)Seminars on Stochastic Processes 1981, 1982, 1983,1984 (four volumes), Birkhäuser, Boston.
[1] Clark, J. M. C.The representation of functionals of Brownian motion by stochastic integrals, Ann. Math. Stat., 41, 1282-1295 (1970); 42, 1778 (1971).
[2] Clark, J. M. C.An introduction to stochastic differential equations on manifolds, in Geometric Methods in Systems Theory (eds. D. Q., Mayne and R. W., Brockett), Reidel, Dordrecht, 1973.
[3] Clark, J. M. C.The design of robust approximations to the stochastic differential equations of nonlinear filtering, in Communication Systems and Random Process Theory (ed. J., Skwirzynski), Sijthoff and Noordhoff, Alphen an den Rijn, 1978.
[1] Clarkson, B. (editor) Stochastic problems in dynamics, Pitman, London, 1977.
[1] Cocozza, C. and Yor, M.Démonstration simplifiée d'un théorème de Knight, Séminaire de Probabilités XIV: Lecture Notes in Mathematics 721, Springer, Berlin, 1980, pp. 496–499.
[1] Cranston, M.Means of approach of two-dimensional Brownian motion (to appear in Ann. Probab).
[1] Cutland, N.Non-standard measure theory and its applications, Bull. London Math. Soc, 15, 529–589 1983.
[1] Cutland, N. and Kendall, W. S.A non-standard proof of one of David Williams' splitting-time theorems, in D. G., Kendall [5], pp. 37–48.
[1] Darling, R. W. R.Martingales in manifolds-definition, examples, and behaviour under maps, Séminaire de Probabilités X VI Supplement: Lecture Notes in Mathematics 921, Springer, Berlin, 1982, pp. 217–236.
[1] Da Vies, E. B. and Simon, B.Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Fund. Anal. 59, 335-395 (1984).
[1] Davies, B.Picard's theorem and Brownian motion, Trans. Amer. Math. Soc, 213, 353–362 1975.
[1] Davis, M. H. A.On a multiplicative functional transformation arising in non-linear filtering theory, Z. Wahrscheinlichkeitstheorie, 54, 125–139 1980.
[2] Davis, M. H. A.Pathwise non-linear filtering, in Stochastic Systems: the Mathematics of Filtering and Identification and Applications (eds. M., Hazewinkel and J. C., Willems), Reidel, Dordrecht, 1981.
[3] Davis, M. H. A.Some current issues in stochastic control theory, Stochastics.
[1] Davis, M. H. A. and Varaiya, P.Dynamic programming conditions for partially observed stochastic systems, SI AM J. Control, 11, 226–261 1973.
[1] Dawson, D. A. and Gärtner, J.Large deviations from the McKean-Vlasov limit for weakly-interacting diffusions, Stochastics, 20, 247–308 1987.
[1] Dellacherie, C.Capacités et Processus Stochastiques, Springer, Berlin, 1972.
[2] Dellacherie, C.Quelques exemples familiers en probabilités d'ensembles analytiques non-Boréliens, Séminaire de Probabilités XII: Lecture Notes in Mathematics, Springer, Berlin, 1978, pp. 742-745.
[3] Dellacherie, C.Un survoi de la théorie de l'intégrale stochastique, Stock Proc. Appt., 10, 115–144 1980.
[1] Dellacherie, C., Doleans-Dade, Catherine, Letta, G. and Meyer, P.-A.Diffusions à coefficients continus d'après D. W. Stroock et S. R. S. Varadhan, Séminaire de probabilités IV: Lecture Notes in Mathematics 124, Springer, Berlin, 1970, pp. 241-282.
[1] Dellacherie, C. and Meyer, P. A.Probabilités et Potentiel, Chaps. I-VI, Hermann, Paris, 1975; Chaps. V-VIII, Hermann, Paris, 1980; Chaps. IX-XI, Hermann, Paris, 1983; Chapters XII-XVI (1987).
[1] De Witt-Morette, Cecile and Elworthy, K. D. (editors)New stochastic methods in physics, Physics Reports, 77, (3), 121-382 (1981).
[1] Doleans-Dade, CatherineExistence du processus croissant naturel associé à un potentiel de la classe (D), Z. Wahrscheinlichkeitstheorie, 9, 309–314 1968.
[2] Doleans-Dade, CatherineQuelques applications de la formule de changement de variables pour les semimartingales, Z. Wahrscheinlichkeitsth., 16, 181–194 1970.
[1] Doleans-Dade, C. and Meyer, P. A.Equations différentielles stochastiques, Sém. de Probabilités XI: Lecture Notes in Mathematics 581, Springer, Berlin, 1977, pp. 376–382.
[1] Doob, J. L.Stochastic Processes, Wiley, New York, 1953.
[2] Doob, J. L.State-spaces for Markov chains, Trans. Am. Math. Soc, 149, 279–305 1970.
[3] Doob, J. L.Classical Potential Theory and its Probabilistic Counterpart, Springer, New York, 1981.
[1] Doss, H.Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. Henri Poincaré B, 13, 99–126 1977.
[1] Dubins, L. and Schwarz, G.On continuous martingales, Proc Nat. Acad. Sci. USA, 53, 913–916 1965.
[1] Dunford, N. and Schwartz, J. T.Linear operators: Part I, General Theory, Interscience, New York, 1958.
[1] Durrett, R.Brownian Motion and Martingales in Analysis, Wadsworth, Belmont, Ca., 1984.
[2] Durrett, R.(Editor) Particle systems, random media, large deviations, Contemporary Maths. 41, Amer. Math. Soc., Providence, RI, 1985.
[1] Dynkin, E. B.Theory of Markov Processes, English translation, Pergamon Press, Oxford, 1960.
[2] Dynkin, E. B.Markov Processes, English translation in two volumes, Springer, Berlin, 1965.
[3] Dynkin, E. B.Non-negative eigenfunctions of the Laplace-Beltrami operator and Brownian motion in certain symmetric spaces (in Russian), Doki. Akad. Naud SSSR, 141, 288-291 (1961).
[4] Dynkin, E. B.Diffusion of tensors, Dokl. Acad. Nauk. SSSR, 179, 1264–1267 1968.
[5] Dynkin, E. B.Local times and quantum fields, in Çinlar, Chung and Getoor [1, 1983].
[6] Dynkin, E. B.Gaussian and non-Gaussian random fields associated with Markov processes, J. Fund. Anal., 55, 344–376 1984.
[7] Dynkin, E. B.Self-intersection local times, occupation fields and stochastic integrals, (to appear in Advances in Appl. Math.).
[1] Elliott, R. J.Stochastic Calculus and Applications, Springer, Berlin, 1982.
[1] Elliott, R. J. and Anderson, B. D. O.Reverse time diffusions, Stochastic Processes and their Applications, 19, 327–339 1985.
[1] Elworthy, K. D.Stochastic Differential Equations on Manifolds, London Mathematical Society Lecture Note Series 20, Cambridge University Press, Cambridge, 1982.
[2] Elworthy, K. D.(Editor) From local times to global geometry, control and physics, Proceedings, Warwick Symposium 1984/85, Longman, Harlow and Wiley, New York, 1986.
[1] Elworthy, K. D. and Stroock, D. W.Large deviation theory for mean exponents of stochastic flows, Appendix to Carverhill, Chappell and Elworthy [1].
[1] Elworthy, K. D. and Truman, A.Classical mechanics, the diffusion (heat) equation and the Schrödinger equation on a Riemannian manifold, J. Math. Phys., 22, (10), 2144-2166 (1981).
[2] Elworthy, K. D. and Truman, A.The diffusion equation and classical mechanics: an elementary formula, in Stochastic processes in quantum theory and statistical physics (ed. S., Albeverio et al.), Lecture Notes in Physics, 173, Springer, Berlin, 1982, pp. 136–146.
[1] Emery, M.Annoncabilité des temps previsibles: deux contre-exemples, Séminaire de Probabilités IV: Lecture Notes in Mathematics 784, Springer, Berlin, 1980, pp. 318–323.
[1] Ethier, S. N. and Kurtz, T. G.Markov Processes: Characterization and Convergence, Wiley, New York, 1986.
[1] Feller, W.Introduction to Probability Theory and its Applications, Vol. 1, 2nd edn., Wiley, New York, 1957; Vol. 2, Wiley, New York, 1966.
[2] Feller, W.Boundaries induced by non-negative matrices, Trans. Am. Math. Soc., 83, 19-54 (1956).
[3] Feller, W.On boundaries and lateral conditions for the Kolmogorov equations, Ann. Math., Ser. II, 65, 527-570 (1957).
[4] Feller, W.Generalized second-order differential operators and their lateral conditions, Illinois J. Math., 1, 459–504 1957.
[1] Fleming, W. H. and Rishel, R. W.Deterministic and Stochastic Optimal Control, Springer, Berlin, 1975.
[1] Föllmer, H.Calcul d'lto sans probabilités, Sem. de Probabilités X V: Lecture Notes in Mathematics 850, Springer, Berlin, 1981, pp. 143–150.
[1] Freedman, D.Brownian Motion and Diffusion, Holden-Day, San Francisco, 1971.
[2] Freedman, D.Approximating Countable Markov Chains, Holden-Day, San Francisco, 1972.
[1] Friedman, A.Stochastic Differential Equations and Applications, in two volumes, Academic Press, New York, 1975.
[1] Fujisaki, M., Kallianpur, G. and Kunita, H.Stochastic differential equations for the non-linear filtering problem, Osaka J. Math., 9, 19–40 1972.
[1] Fukushima, M.Dirichlet Forms and Markov Processes, Kodansha, Tokyo, 1980.
[2] Fukushima, M.Basic properties of Brownian motion and a capacity on the Wiener space, J. Math. Soc. Japan, 36, 161–176 1984.
[1] Garcia Alvarez, M. A. and Meyer, P. A.Une théorie de la dualité à un ensemble polaire près: I, Ann. Prob., 1, 207–222 1973.
[1] Garsia, A.Martingale Inequalities: Seminar Notes on Recent Progress, Benjamin, Reading, Ma., 1973.
[1] Geman, D. and Horowitz, J.Occupation densities, Ann. Prob., 8, 1–67 1980.
[1] Geman, D., Horowitz, J. and Rosen, J.A local time analysis of intersections of Brownian paths in the plane, Ann. Prob., 12, 86–107 1984.
[1] Getoor, R. K.Markov processes: Ray Processes and Right Processes: Lecture Notes in Mathematics 440, Springer, Berlin, 1975.
[2] Getoor, R. K.Excursions of a Markov process, Ann. Prob., 8, 244–266 1979.
[3] Getoor, R. K.Splitting times and shift functionals Z. Wahrscheinlichkeitstheorie, 47, 69–81 1979.
[1] Getoor, R. K. and Sharpe, M. J.Last exit times and additive functionals, Ann. Prob., 1, 550–569 1973.
[2] Getoor, R. K. and Sharpe, M. J.Excursions of Brownian motion and Bessel process, Z. Wahrscheinlichkeitstheorie, 47, 83–106 1979.
[3] Getoor, R. K. and Sharpe, M. J.Last exit decompositions and distributions, Indiana Univ. Math. J., 23, 377–404 1973.
[4] Getoor, R. K. and Sharpe, M. J.Excursions of dual processes, Advances in Math., 45, 259–309 1982.
[1] Gikhman, I.I., and Skorokhod, A. V.The Theory of Stochastic Processes (three volumes), Springer, Berlin, 1979.
[1] Gray, A., Karp, L. and Pinsky, M. A.The mean exit time from a ball in a Riemannian manifold.
[1] Gray, A. and Pinsky, M. A.The mean exit time from a small geodesic ball in a Riemannian manifold, Bull. Sc. Math., 107, 345–370 1983.
[1] Greenwood, P. and Pitman, J. W.Construction of local time and Poisson point processes from nested arrays, J. London Math. Soc. (2), 22, 182-192 (1980).
[2] Greenwood, P. and Pitman, J. W.Fluctuation identities for Levy processes and splitting at the maximum, Adv. Appl. Prob., 12, 893–902 1980.
[1] Grenander, U.Probabilities on Algebraic Structures, Wiley, New York, 1963.
[1] Griffeath, D.Coupling methods for Markov processes, in Advances in Mathematics Supplementary Studies: Studies in Probability and Ergodic Theory, Vol. 2, Academic Press, New York, 1978, pp. 1–43.
[1] Gromov, M. and Rohlin, V. A.Russian Math. Surveys, 25, 1–57 1970.
[1] Halmos, P.Measure Theory, Van Nostrand, Princeton, NJ, 1959.
[1] Haussmann, U.On the integral representation of Ito processes, Stochastics, 3, 17–27 1979.
[2] Haussmann, U.A stochastic maximum principle for optimal control of diffusions, Longman, Harlow, 1986.
[1] Hawkes, J.Multiple points for symmetric Levy processes, Math. Proc. Camb. Phil., 83, 83–90 1978.
[2] Hawkes, J.The measure of the range of a subordinator, Bull. London Math. Soc., 5, 21-28 (1973).
[1] Hazewinkel, M. and WILLEMS, J. C. (editors)Stochastic Systems: the Mathematics of Filtering and Identification and Applications, Reidel, Dordrecht, 1981.
[1] Helgason, S.Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962.
[1] Hille, E. and Phillips, R. S.Functional Analysis and Semigroups, American Mathematical Society Colloquium Publications, Providence, RI, 1957.
[1] Holley, R., Stroock, D. W. and Williams, D.Applications of dual processes to diffusion theory, Proc. AMS Prob. Symp., Urbana, 1976, pp. 23–36.
[1] Hormander, L.Hypoelliptic second-order differential equations, Acta Math., 117, 147–171 1967.
[1] Hsu, P.On excursions of reflecting Brownian motion, Trans. Amer. Math. Soc., 296, 239-264 (1986).
[2] Hsu, P.Brownian motion and the index theorem (to appear).
[1] Hunt, G. A.Markoff processes and potentials: I, II, III, Illinois J. Math., 1, 44-93; 316-369 (1957); 2, 151-213 (1958).
[1] Ikeda, N. and Watanabe, S.Stochastic Differential Equations and Diffusion Processes, North Holland-Kodansha, Amsterdam and Tokyo, 1981.
[2] Ikeda, N. and Watanabe, S.Malliavin calculus of Wiener functionals and its applications, in Elworthy [2], pp. 132–178.
[1] Itô, K.Stochastic integral, Proc. Imp. Acad. Tokyo, 20, 519–524 1944.
[2] Itô, K.On a stochastic integral equation, Proc. Imp. Acad. Tokyo, 22, 32–35 1946.
[3] Itô, K.Stochastic differential equations in a differential manifold, Nagoya Math. J., 1, 35-47 (1950).
[4] Itô, K.The Brownian motion and tensor fields on a Riemannian manifold, Proc. Intern. Congr. Math., Stockholm, 1963, pp. 536–539.
[5] Itô, K.Stochastic parallel displacement, in Probabilistic Methods in Differential Equations: Lecture Notes in Mathematics 451, Springer, Berlin, 1975, pp. 1–7.
[6] Itô, K.Poisson point processes attached to Markov processes, Proc. 6th Berkeley Symp. Math. Statist. Prob., Vol. 3, University of California Press, 1971, pp. 225–240.
[7] Itô, K.(editor) Proceedings of the 1982 Taniguchi Intern. Symp. on Stochastic Analysis, Kinokuniya-Wiley, 1984.
[1] Itô, K. and McKean, H. P.Diffusion Processes and their Sample Paths, Springer, Berlin, 1965.
[1] Jacka, S.A finite fuel stochastic control problem, Stochastics, 10, 103–113 1983.
[2] Jacka, S.A local time inequality for martingales, Sem. de Probabilités X VII: Lecture Notes in Mathematics 986, Springer, Berlin, 1983.
[1] Jacobsen, M.Splitting times for Markov processes and a generalised Markov property for diffusions, Z. Wahrscheinlichkeitstheorie, 30, 27–43 1974.
[2] Jacobsen, M.Statistical Analysis of Counting Processes: Lecture Notes in Statistics 12, Springer, New York, 1982.
[1] Jacod, J.A general theorem of representation for martingales, Proc. AMS Prob. Symp., Urbana, 1976, pp. 37–53.
[2] Jacod, J.Calcul Stochastique et Problèmes de Martingales: Lecture Notes in Mathematics 714, Springer, Berlin, 1979.
[1] Jacod, J. and Yor, M.Etude des solutions extrémales et représentation intégrale des solutions pour certains problèmes de martingales, Z. Wahrscheinlichkeitsth., 38, 83–125 1977.
[1] Jeulin, T.Semimartingales et Grossissement d'une Filtration: Lecture Notes in Mathematics 833, Springer, Berlin, 1980.
[1] Jeulin, T. and Yor, M.Grossissement d'une filtration et semi-martingales: formules explicites, Séminaire de Probabilités XII: Lecture Notes in Mathematics 649, Springer, Berlin, 1978, pp. 78–97.
[2] Jeulin, T. and Yor, M.(editors) Grossissements de Filtrations: Examples et Applications: Lecture Notes in Mathematics 1118, Springer, Berlin, 1985.
[1] Johnson, G. and Helms, L. L.Class (D) supermartingales, Bull. Amer. Math. Soc, 69, 59–62 1963.
[1] Kailath, T.An innovations approach to least squares estimation, Part I: Linear filtering with additive white noise, IEEE Trans. Automatic Control, 13, 646–655 1968.
[1] Kallianpur, G.Stochastic Filtering Theory, Springer, Berlin, 1980.
[1] Kendall, D. G.Pole-seeking Brownian motion and bird navigation (with discussion), J. Roy. Statist. Soc. B, 36, 365-417 (1974).
[2] Kendall, D. G.The diffusion of shape, Adv. Appl. Prob., 9, 428–430 (1979).
[3] Kendall, D. G.Shape manifolds, Procrustean metrics, and complex projective spaces, Bull. London Math. Soc, 16, 81–121 1984.
[4] Kendall, D. G.A totally unstable Markov process, Quarterly J. Math. Oxford, 9, (34), 149-160(1958).
[5] Kendall, D. G. (Editor) Analytic and geometric stochastics (special supplement to Adv. Appl. Prob. to honour G. E. H. Reuter), Applied Prob. Trust, 1986.
[1] Kendall, D. G. and Reuter, G. E. H.Some pathological Markov processes with a denumerable infinity of states and the associated contraction semigroups of operators on l, Proc. Intern. Congress Math. 1954 (Amsterdam), 3, 377–415 (1956).
[1] Kendall, W. S.Knotting of Brownian motion in 3-space, J. London Math. Soc. (2), 19, 378-384 (1979).
[2] Kendall, W. S.Brownian motion, negative curvature, and harmonic maps. Stochastic Integrals: Lecture Notes in Mathematics 851, Springer, Berlin, 1981, pp. 479-491.
[3] Kendall, W. S.Brownian motion on a surface of negative curvature, Séminaire de probabilités XVIII: Lecture Notes in Mathematics 1059, Springer, Berlin, 1984, pp. 70-76.
[4] Kendall, W. S.Survey article on stochastic differential geometry (to appear).
[1] Kent, J.Some probabilistic properties of Bessel functions, Ann. Prob., 6, 760–770 1978.
[2] Kent, J.The infinite divisibility of the von Mises-Fisher distribution for all values of the parameter in all dimensions. Proc. London Math. Soc., 3, (35), 359-384 (1977).
[1] Khasminskii, R. Z.Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations, Th. Prob. and Appl., 5, 179–196 1960.
[2] Khasminskii, R. Z.Stochastic stability of differential equations, Sijthoff and Noordhoff, Alphen aan den Rijn, 1980.
[1] Kifer, Y.Brownian motion and positive harmonic functions on complete manifolds of non-positive curvature, in Elworthy [2], pp. 187–232.
[1] Kingman, J. F. C.Subadditive ergodic theory, Ann. Prob., 1, 883–909 1973.
[2] Kingman, J. F. C.Completely random measures, Pacific J. Math., 21, 59–78 1967.
[3] Kingman, J. F. C.Regenerative Phenomena, Wiley, New York, 1972.
[1] Knight, F. B.Note on régularisation of Markov processes, Illinois J. Math., 9, 548-552 (1965).
[2] Knight, F. B.A reduction of continuous square-integrable martingales to Brownian motion, in Martingales: a Report on a Meeting at Oberwolfach (ed. H. Dinges): Lecture Notes in Mathematics 190, Springer, Berlin, 1971, pp. 19-31.
[3] Knight, F. B.Random walks and the sojourn density process of Brownian motion, Trans. Amer. Math. Soc, 107, 56–86 1963.
[1] Knight, F. B. and Pittenger, A. O.Excision of a strong Markov process, Z. Wahrscheinlichkeitsth., 23, 114–120 1972.
[1] Kobayashi, S. and Nomizu, K.Foundations of Differential Geometry, Wiley-Interscience, New York, 1969.
[1] Kozin, F. and Prodromou, S.Necessary and sufficient conditions for almost sure sample stability of linear Itô equations, SIAM J. Appl. Math., 21, 413–425 (1971).
[1] Krylov, N. V.Controlled Diffusion Processes, Springer, New York, 1980.
[1] Kuelbs, J.The law of the iterated logarithm for Banach space valued random variables, in Probability in Banach Spaces: Lecture Notes in Mathematics 526, Springer, Berlin, 1976, pp. 131–142.
[1] Kunita, H.On the decomposition of the solutions of stochastic differential equations, in Stochastic Integrals: Lecture Notes in Mathematics 851, Springer, Berlin, 1981, pp. 213–255.
[2] Kunita, H.On backward stochastic differential equations, Stochastics, 6, 293–313 1982.
[3] Kunita, H.Stochastic differential equations and stochastic flows of homeomorphisms.
[4] Kunita, H.Stochastic partial differential equations connected with nonlinear filtering, in Mitter and Moro [1].
[1] Kunita, H. and Watanabe, S.On square integrable martingales, Nagoya Math. J., 30, 209–245 1967.
[1] Kunita, H. and Watanabe, T.Some theorems concerning resolvents over locally compact spaces, in Proc. 5th Berkeley Symp. Math. Statist. Prob., Vol. 2, Part 2, University of California Press, 1967, pp. 131–164.
[2] Kunita, H. and Watanabe, T.Markov processes and Martin boundaries, I, Illinois J. Math., 9, 485–526 1965.
[3] Kunita, H. and Watanabe, T.On certain reversed processes and their application to potential theory and boundary theory, J. Math. Mech., 15, 393–434 1966.
[1] Kusuoka, S. and Stroock, D.Applications of the Malliavin calculus, Part I, Proceedings of the 1982 Taniguchi Intern. Symp. on Stochastic Analysis (ed. K., Itô), Kinokuniya-Wiley, 1984, pp. 271–306.
[2] Kusuoka, S. and Stroock, D.Applications of the Malliavin calculus, Part II, J. Fac. Sci. U. of Tokyo (IA), 32, 1-76 (1985).
[1] Le Gall, J.-F.Applications du temps local aux equations différentielles stochastiques unidimensionelles, Séminaire de Probabilités X VII: Lecture Notes in Mathematics 986, Springer, Berlin, 1983, pp. 15–31.
[2] Le Gall, J.-F.Sur la saucisse de Wiener et les points multiples du mouvement Brownien, Ann. Prob., 14, 1219–1244 1986.
[3] Le Gall, J.-F.Sur les temps local d'intersection du mouvement Brownien plan et la méthode de renormalization de Varadhan, Séminaire de Probabilités XIX: Lecture Notes in Mathematics 1123, Springer, Berlin, 1985, pp. 314–331.
[1] Lenglart, E., Lepingle, D. and Pratelli, M.Présentation unifiée de certaines inégalités de la théorie des martingales, Séminaire de Probabilités XIV: Lecture Notes in Mathematics 784, Springer, Berlin, 1980.
[1] Levy, P.Théorie de l'Addition des Variables Aléatoires, Gauthier Villars, Paris, 1954.
[2] Levy, P.Processus Stochastiques et Mouvement Brownien, Gauthier Villars, Paris, 1965.
[3] Levy, P.Systèmes markoviens et stationnaires. Cas dénombrable, Ann. Ecole Norm. Sup. (3), 68, 327-381 (1951); 69, 203-212 (1952).
[4] Levy, P.Processus markoviens et stationnaires due cinquième type (infinité dénombrable des états possibles, paramètre continu). C. R. Acad. Sci. Paris, 236, 1630–1632 1953.
[5] Levy, P.Processus markoviens et stationnaires. Cas dénombrable. Ann. Inst H. Poincaré, 16, 7–25 1958.
[1] Lewis, J. T.Brownian motion on a submanifold of Euclidean space, Bull. London Math. Soc., 18, 616–20 1986.
[1] Liggett, T.Interacting Particle Systems, Springer, New York, 1985.
[1] Lindvall, T.On coupling of diffusion processes, J. Appl. Probab., 20, 82–93 1983.
[1] Lipster, R. S. and Shiryayev, A. N.Statistics of Random Processes, I (English translation), Springer, Berlin, 1977.
[1] London, R. R., McKean, H. P., Rogers, L. C. G. and Williams, D.A martingale approach to some Wiener-Hopf problems, I, Séminaire de Probabilités XVI: Lecture Notes in Mathematics 920, Springer, Berlin, 1982, pp. 41–67.
[1] Lyons, T. J.Finely holomorphic functions, J. Funct. Anal., 37, 1–18 1980.
[2] Lyons, T. J.Instability of the Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains, (to appear).
[3] Lyons, T. J.The critical dimension at which quasi-every path is self-avoiding, in D. G., Kendall [5], pp. 87–100.
[1] Lyons, T. J. and McKean, H. P.Windings of the plane Brownian motion. Adv. Math., 51, 212–225 1984.
[1] Maisonneuve, B.Systèmes régéneratifs, Asterique, 15, Société Mathématique de France, 1974.
[1] Maisonneuve, B. and Meyer, P.-A.Ensembles aléatoires markoviens homogènes, in Séminaire de probabilités VIII: Lecture Notes in Mathematics 381, Springer, Berlin, 1974, pp. 172–261.
[1] Malliavin, P.Stochastic calculus of variation and hypo-elliptic operators, Proc. Intern. Symp. Stoch. Diff. Equations, Kyoto, 1976 (ed. K., Itô), Kinokuniya-Wiley, 1978, pp, 195-263.
[2] Malliavin, P.Ck-hypoellipticity with degeneracy, in Stochastic Analysis (ed. A., Friedman and M., Pinsky), Academic Press, New York, 1978, pp. 199-214.
[3] Malliavin, P.Formule de la moyenne, calcul de perturbations et théorèmes d'annulation pour les formes harmoniques, J. Funct. Anal., 17, 274–291 1974.
[1] Malliavin, M. P. and Malliavin, P.Factorisations et lois limites de la diffusion horizontale au dessus d'un espace riemmanien symmetrique, Lecture Notes in Mathematics 404, Springer, Berlin, 1974, pp. 166–217.
[1] Martin, R. S.Minimal positive harmonie functions, Trans. Am. Math. Soc, 49, 137–164 1941.
[1] McGill, P.Calculation of some conditional excursion formulae, Z. Wahrscheinlichkeitstheorie, 61, 255–260 1982.
[2] McGill, P.Markov properties of diffusion local time: a martingale approach, Adv. Appl. Prob., 14, 789–810 1980.
[3] McGill, P.Integral representation of martingales in the Brownian excursion filtration, Séminaire de Probabilités XX: Lecture Notes in Mathematics 1204, Springer, Berlin, 1986, pp. 465–502.
[1] McKean, H. P.Stochastic Integrals, Academic Press, New York, 1969.
[2] McKean, H. P.Excursions of a non-singular diffusion, Z. Wahrscheinlichkeitstheorie, 1, 230–239 1963.
[3] McKean, H. P.Brownian local times, Adv. Math., 16, 91–111 1975.
[1] McNamara, J. M.A regularity condition on the transition probability measure of a diffusion process. Stochastics, 15, 161–182 1985.
[1] Mandl, P.Analytic Treatment of One-Dimensional Markov Processes, Springer, Berlin, 1968.
[1] Meleard, S.Application du calcul stochastique à l'étude de processus de Markov réguliers sur [0,1], Stochastics, 19, 41–82 1986.
[1] Metivier, M. and Pellaumail, J.Stochastic Integration, Academic Press, New York, 1979.
[1] Meyer, P. A.Un cours sur les intégrales stochastiques, Séminaire de Probabilités X: Lecture Notes in Mathematics 511, Springer, Berlin, 1976, pp. 245-400.
[2] Meyer, P. A.Probability and Potential (English translation), Blaisdell, Waltham, Mass., 1966.
[3] Meyer, P. A.Processus de Markov: Lecture Notes in Mathematics 26, Springer, Berlin, 1967.
[4] Meyer, P. A.Processus de Markov: la Frontière de Martin: Lecture Notes in Mathematics 77, Springer, Berlin, 1970.
[5] Meyer, P. A.Démonstration simplifiée d'un théorème de Knight, Sém. de Probabilités V: Lecture Notes in Mathematics 191, Springer, Berlin, 1971, pp. 191-195.
[6] Meyer, P. A.Démonstration probabiliste de certaines inégalités de Littlewood-Paley, Sém. de Probabilités X: Lecture Notes in Mathematics 511, Springer, Berlin, 1976, pp. 125–183.
[7] Meyer, P. A.Flot d'un equation différentielle stochastique, Sèm. de Probabilités XV: Lecture Notes in Mathematics 850, Springer, Berlin, 1981, pp. 103–117.
[8] Meyer, P. A.Sur la démonstration de prévisibilité de Chung and Walsh, Sém. de Probabilités IX: Lecture Notes in Mathematics 465, Springer, Berlin, 1975, pp. 530–533.
[9] Géométrie stochastique sans larmes, Séminaire de Probabilités X V: Lecture Notes in Mathematics 850, Springer, Berlin, 1981, pp. 44-102.
[10] Meyer, P. A.Géométrie stochastique sans larmes (bis), Séminaire de Probabilités XVI: Supplément, Lecture Notes in Mathematics 921, Springer, Berlin, 1982, pp. 165–207.
[11] Meyer, P. A.Eléments de probabilités quantiques, Séminaire de Probabilités XX: Lecture Notes in Mathematics 1204, Springer, Berlin, 1986, pp. 186–312.
[1] Mihlstein, G. N.Approximate integration of stochastic differential equations, Th. Prob. Appl., 19, 557–562 1974.
[1] Millar, P. W.Random times and decomposition theorems, in Probability: Proc. Symp. Pure Math. XXXI, American Mathematical Society, Providence, RI, 1977, pp. 91-103.
[2] Millar, P. W.A path decomposition for Markov processes, Ann. Prob., 6, 345–348 1978.
[1] Mitter, S. K.Lectures on non-linear filtering and stochastic control, in Mitter and Moro [1], pp. 170–207.
[1] Mitter, S. K. and Moro, A. (editors) Non-linear filtering and stochastic control, Lecture Notes in Mathematics 972, Springer, Berlin, 1982.
[1] Motoo, M.Application of additive functionals to the boundary problem of Markov processes (Levy's system of U-processes), Proc. Fifth Berkeley Symposium Math. Statist. Prob. 11(2), Univ. Calif. Press, Berkeley, 1967, pp. 75–110.
[1] Motoo, M. and Watanabe, S.On a class of additive functionals of Markov processes, J. Math. Kyoto Univ., 4, 429–469 (1965).
[1] Nakao, S.On the path wise uniqueness of solutions of one-dimensional stochastic differential equations, Osaka J. Math., 9, 513–518 1972.
[1] Nash, J. F.The imbedding problem for Riemannian manifolds, Ann. of Math., 63, 20-63 (1956).
[1] Nelson, E.Dynamical Theories of Brownian Motion, Princeton Univ. Press, 1967.
[2] Nelson, E.Quantum Fluctuations, Princeton Univ. Press, 1984.
[1] Neveu, J.Bases Mathématiques du Calcul des Probabilités, Masson, Paris, 1964.
[2] Neveu, J.Sur les états d'entrée et les états fictifs d'un processus de Markov, Ann. Inst. Henri Poincaré, 17, 323–337 1962.
[3] Neveu, J.Lattice methods and submarkovian processes, Proc. 4th Berkeley Symp. Math. Statist. Prob., Vol. 2, University of California Press, 1960, pp. 347-391.
[4] Neveu, J.Une généralisation des processus à accroissements positifs indépendants, Abh. Math. Sem. Univ. Hamburg, 25, 36–61 1961.
[5] Neveu, J.Entrance, exit and fictitious states for Markov chains, Proc. Aarhus Colloq. Combin. Prob., 1962, pp. 64–68.
[1] Norris, J. R.Simplified Malliavin calculus, Séminaire de Probabilités XX: Lecture Notes in Mathematics 1204, Springer, Berlin, 1986, pp. 101–130.
[1] Norris, J. R., Rogers, L. C. G. and Williams, D.Brownian motion of ellipsoids, Trans. Amer. Math. Soc, 294, 757–765 1986.
[2] Norris, J. R., Rogers, L. C. G. and Williams, D.Self-avoiding random walk: a Brownian motion model with local time drift, Prob. Thy. and Rel. Fields, 74, 271–287 1987.
[1] Ocone, D.Malliavin's calculus and stochastic integral: representation of functionals of diffusion processes, Stochastics, 12, 161–185 1984.
[1] Orihara, A.On random ellipsoid, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 17, 73–85 1970.
[1] Pardoux, E.Stochastic differential equations and filtering of diffusion processes, Stochastics, 3, 127–167 1979.
[2] Pardoux, E.Grossissement d'une filtration et retournement du temps d'une diffusion, Sém. de Probabilités XX: Lecture Notes in Mathematics 1204, Springer, Berlin, 1986, pp. 48–55.
[3] Pardoux, E.Equations of non-linear filtering, and applications to stochastic control with partial observations, in Mitter and Moro [1], pp. 208–248.
[1] Pardoux, E. and Talay, D.Discretization and simulation of stochastic differential equations, to appear in Acta Appl. Math.
[1] Parthasarathy, K. R.Probability Measures on Metric Spaces, Academic Press, New York, 1967.
[1] Pauwels, E. and Rogers, L. C. G.Paper on Brownian motions on homogeneous spaces (to appear).
[1] Perkins, E.Local time and path wise uniqueness for stochastic differential equations, Sém. de Probabilités XVI: Lecture Notes in Mathematics 920, Springer, Berlin, 1982, pp. 201–208.
[2] Perkins, E.Local time is a semimartingale Z. Wahrscheinlichtkeitsth., 60, 79–117 1982.
[1] Phelps, R. R.Lectures on Choque's Theorem, Van Nostrand, Princeton, NJ, 1966.
[1] Pinsky, M. A.Homogenization and stochastic parallel displacement, in Williams [13], pp. 271–284.
[2] Pinsky, M. A.Stochastic Riemannian geometry, in Probabilistic Analysis and Related Topics, 1 (ed. A. T., Bharucha-Reid), Academic Press, New York, 1978.
[1] Pitman, J. W.One-dimensional Brownian motion and the three-dimensional Bessel process, J. Appl. Prob., 7, 511–526 1975.
[2] Pitman, J. W.Path decomposition for conditional Brownian motion, Inst. Math. Statist. Univ. Copenhagen, Preprint No. 11 (1974).
[3] Pitman, J. W.Levy systems and path decompositions, in Çinlar, Chung and Getoor [1, 1981].
[1] Pitman, J. W. and Yor, M.Bessel processes and infinitely divisible laws, in Stochastic Integrals (ed. D. Williams), Lecture Notes in Mathematics 851, Springer, Berlin, 1981.
[2] Pitman, J. W. and Yor, M.A decomposition of Bessel bridges. Z. Wahrscheinlichkeitsth., 59, 425–457 1982.
[3] Pitman, J. W. and Yor, M.The asymptotic joint distribution of windings of planar Brownian motion, Bull. Amer. Math. Soc, 10, 109–111 1984.
[4] Pitman, J. W. and Yor, M.Asymptotic laws of planar Brownian motion, Ann. Probab., 14, 733–779 1986.
[1] Pittenger, A. O. and Shih, C. T.Coterminal families and the strong Markov property, Trans. Amer. Math. Soc, 182, 1–42 1973.
[1] Poor, W. A.Differential Geometric Structures, McGraw-Hill, New York, 1981.
[1] Port, S. C. and Stone, C. J.Classical potential theory and Brownian motion, Proc. 6th Berkeley Symp. Math. Statist. Prob., Vol. 3, University of California Press, 1972, pp. 143–176.
[2] Port, S. C. and Stone, C. J.Logarithmic potentials and planar Brownian motion, Proc. 6th Berkeley Symp. Math. Statist. Prob., Vol. 3, University of California Press, 1972, pp. 177-192.
[3] Port, S. C. and Stone, C. J.Brownian Motion and Classical Potential Theory, Academic Press, New York, 1978.
[1] Price, G. C. and Williams, D.Rolling with ‘slipping’: I, Sém. de Probabilités XVII: Lecture Notes in Mathematics 986, Springer, Berlin, 1983, pp. 194–197.
[1] Prohorov, Yu. V.Convergence of random processes and limit theorems in probability, Theor. Prob. Applic, 1, 157–214 1956.
[1] Protter, P.On the existence, uniqueness, convergence and explosions of solutions of stochastic differential equations, Ann. Probab., 5, 243–261 1977.
[1] Rao, K. M.On decomposition theorems of Meyer, Math. Scand., 24, 66–78 1969.
[2] Rao, K. M.Quasimartingales, Math. Scand., 24, 79–92 1969.
[1] Ray, D. B.Resolvents, transition functions and strongly Markovian processes, Ann. Math., 70, 43–72 1959.
[2] Ray, D. B.Sojourn times of a diffusion process, Illinois J. Math., 7, 615–630 1963.
[1] Reuter, G. E. H.Denumerable Markov processes, II, J. London Math. Soc, 34, 81–91 1959.
[1] Revuz, D.The Martin boundary of a recurrent random walk has one or two points, in Probability: Proc. Symp. Pure Math. XXXI, American Mathematical Society, Providence, RI, 1977, pp. 125–130.
[1] Rogers, L. C. G.Williams' characterization of the Brownian excursion law: proof and applications, Séminaire de Probabilités XV: Lecture Notes in Mathematics 850, Springer, Berlin, 1981, pp. 227–250.
[2] Rogers, L. C. G.Itô excursion theory via resolvents, Z. Wahrscheinlichkeitstheorie, 63, 237-255 (1983).
[3] Rogers, L. C. G.Smooth transition densities for one-dimensional diffusions, Bull. London Math. Soc, 17, 157–161 1985.
[4] Rogers, L. C. G.Continuity of martingales in the Brownian excursion filtration, to appear.
[1] Rosen, J.A local time approach to self-intersections of Brownian paths in space, Comm. Math. Phys., 88, 327–338 1983.
[1] Schwartz, L.Geometrie différentielle du 2ième ordre, semimartingales et équations différentielles stochastiques sur une variété différentielle, Sém. de Probabilités XVI: Supplément, Lecture Notes in Mathematics 921, Springer, Berlin, 1982, pp. 1–148.
[1] Sharpe, M. J.Forthcoming book on Markov processes.
[1] Sheppard, P.On the Ray-Knight property of local times, J. London Math. Soc., 31, 377-384 (1985).
[1] Shiga, T. and Watanabe, S.Bessel diffusions as a one-parameter family of diffusion processes, Z. Wahrscheinlichkeitstheorie, 27, 37–46 (1973).
[1] Shigekawa, I.Derivatives of Wiener functionals and absolute continuity of induced measure, J Math. Kyoto Univ., 20, 263–289 1980.
[1] Sllverstein, M. L.Symmetric Markov Processes: Lecture Notes in Mathematics 426, Springer, Berlin 1974.
[2] Sllverstein, M. L.Boundary Theory for Symmetric Markov Processes: Lecture Notes in Mathematics 516, Springer, Berlin, 1976.
[1] Simon, B.Functional Integration and Quantum Physics, Academic Press, New York, 1979.
[2] Simon, B.Paper on tunnelling (to appear, Ann. Inst. H. Poincarel)
[1] Skorokhod, A. V.Limit theorems for stochastic processes, Theor. Prob. Applic, 1, 261–290 1956.
[2] Skorokhod, A. V.Limit theorems for Markov processes, Theor. Prob. Applic, 3, 202–246 1958.
[1] Spitzer, F.Principles of Random Walk, Van Nostrand, Princeton, NJ, 1964.
[1] Strassen, V.An invariance principle for the law of the iterated logarithm, Z. Wahrscheinlichkeitstheorie, 3, 211–226 1964.
[2] Strassen, V.Almost sure behaviour of sums of independent random variables and martingales, Proc. 5th Berkeley Symp. Math. Statist. Prob., Vol. 2, Part 1, University of California Press, 1966, pp. 315–343.
[1] Stroock, D. W.The Malliavin calculus and its applications to second-order parabolic differential operators I, II, Math. System Theory, 14, 25-65, 141-171 (1981).
[2] Stroock, D. W.The Malliavin calculus; a functional analytical approach, J. Fund. Anal., 44, 217-257 (1981).
[3] Stroock, D. W.Diffusion processes associated with Levy generators Z. Wahrscheinlichkeitstheorie, 32, 209–244 1975.
[4] Stroock, D. W.An Introduction to the Theory of Large Deviations, Springer, Berlin, New York, 1984.
[1] Stroock, D. W. and Varadhan, S. R. S.Multidimensional Diffusion Processes, Springer, New York, 1979.
[2] Stroock, D. W. and Varadhan, S. R. S.On the support of diffusion processes with applications to the strong maximum principle, Proc. 6th Berkeley Symp. Math. Statist. Prob., Ill, Univ. Calif. Press, Berkeley, 1972, pp. 333-359.
[3] Stroock, D. W. and Varadhan, S. R. S.Diffusion processes with boundary conditions, Comm. Pure Appl. Math., 24, 147-225 (1971).
[1] Stroock, D. W. and Yor, M.Some remarkable martingales, Sem. de Probabilités XV: Lecture Notes in Mathematics 850, Springer, Berlin, 1981, pp. 590–603.
[1] Sussmann, H. J.On the gap between deterministic and stochastic ordinary differential equations, Ann. Prob., 6, 19–41 (1978).
[1] Taylor, H. M.A stopped Brownian motion formula, Ann. Prob., 3, 234–246 1975.
[1] Taylor, S. J.Sample path properties of processes with stationary independent increments, in Stochastic Analysis, eds D. G., Kendall and E. F., Harding, Wiley, New York, 1973, pp. 387–414.
[1] Tsirelson, B. S.An example of the stochastic equation having no strong solution, Teoria Verojatn. i Primenen., 20, (2), 427-430 (1975).
[1] Van Den Berg, M. and Lewis, J. T.Brownian motion on a hypersurface, Bull. London Math. Soc, 17, 144–150 1985.
[1] Varadhan, S. R. S.Large deviations and applications, SIAM, Philadelphia, 1984.
[1] Walsh, J. B.Excursions and local time, in Azema and Yor [2], pp. 159–192.
[2] Walsh, J. B.Stochastic integration with respect to local time, in Çinlar, Chung and Getoor [1; 1983]
[1] Warner, F. W.Foundations of Differentiable Manifolds and Lie Groups, Springer, Berlin, New York, 1983.
[1] Watanabe, S.On discontinuous additive functionals and Levy measures of a Markov process, Jap. J. Math., 34, 53–79 1964.
[1] Whitney, H.Geometric Integration Theory, Princeton University Press, Princeton, N. J., 1957.
[1] Whittle, P.Optimization Over Time (two volumes), Wiley, Chichester, 1982, 1983.
[1] Williams, D.Brownian motions and diffusions as Markov processes, Bull. London Math. Soc., 6, 257–303 1974.
[2] Williams, D.Some basic theorems on harnesses, in Stochastic Analysis, eds. D. G., Kendall and E. F., Harding, Wiley, New York, 1973, pp. 349-366.
[3] Williams, D.On Levy's downcrossing theorem, Z. Wahrscheinlichkeitstheorie, 40, 157-158 (1977).
[4] Williams, D.Path decomposition and continuity of local time for one-dimensional diffusions, I, Proc. London Math. Soc., Ser. 3, 28, 738-768 (1974).
[5] Williams, D.On a stopped Brownian motion formula of H. M. Taylor, Séminaire de Probabilités X: Lecture Notes in Mathematics 511, Springer, Berlin, 1976, pp. 235-239.
[6] Williams, D.Markov properties of Brownian local time, Bull. Am. Math. Soc., 75, 1035-1036 (1969).
[7] Williams, D.Decomposing the Brownian path, Bull. Am. Math. Soc, 76, 871–873 1970.
[8] Williams, D.The Q-matrix problem for Markov chains, Bull. Am. Math. Soc, 81, 1115–1118 1975.
[9] Williams, D.The Q-matrix problem, Séminaire de Probabilités X: Notes in Mathematics 511, Springer, Berlin, 1976, pp. 216-234.
[10] Williams, D.A note on the Q-matrices of Markov chains, Z. Wahrscheinlichkeitstheorie, 7, 116–121 1967.
[11] Williams, D.Some g-matrix problems, in Probability: Proc Symp. Pure Math. XXXI, American Mathematical Society, Providence, RI, 1977, pp. 165–169.
[12] Williams, D.Diffusions, Markov Processes, and Matingales, Volume 1: Foundations, Wiley, Chichester, New York, 1979.
[13] Williams, D.(editor) Stochastic integrals: Proceedings, LMS Durham Symposium, Lecture Notes in Mathematics 851, Springer, Berlin 1981.
[14] Williams, D.Conditional excursion theory, Sém. de Probabilités XIII: Lecture Notes in Mathematics 721, Springer, Berlin, 1979, 490-494.
[1] Yamada, T.On a comparison theorem for solutions of stochastic differential equations and its applications, J. Math. Kyoto Univ., 13, 497–512 1973.
[1] Yamada, T. and Ogura, Y.On the strong comparison theorems for solutions of stochastic differential equations, Z. Wahrscheinlichkeitstheorie, 56, 3–19 1981.
[1] Yamada, T. and Watanabe, S.On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ., 11, 155–167 1971.
[1] Yor, M.Sur certains commutateurs d'une filtration, Sém. de Probabilités X V: Lecture Notes in Mathematics 850, Springer, Berlin, 1981, pp. 526–528.
[2] Yor, M.Sur la continuité des temps locaux associés à certaines semimartingales, in Azema and Yor [2], pp. 23–35.
[3] Yor, M.Rappel et préliminaires généraux, in Azema and Yor [2], pp. 17–22.
[4] Yor, M.Précisions sur l'existence et la continuité des temps locaux d'intersection du mouvement Brownien dans ℝ2, Sém. de Probabilités XX: Lecture Notes in Mathematics 1204, Springer, Berlin, 1986, pp. 532–542.
[5] Yor, M.Sur la réprésentation comme intégrales stochastiques des temps d'occupation du mouvement Brownien dans ℝ2Sém. de Probabilités XX: Lecture Notes in Mathematics 1204, pp. 543–552.
[1] Yosida, K.Functional Analysis, Springer, Berlin, 1965.
[2] Yosida, K.Brownian motion in homogeneous Riemannian space, Pacific J. Math., 2, 263–296 1952.
[1] Zakai, M.The Malliavin calculus, Acta Appl. Math., 3, 175–207 1985.
[1] Zheng, W. A. and Meyer, P.-A.Quelques résultats de ‘méchanique stochastique’, Sém. de Probabilités X VIII: Lecture Notes in Mathematics 1059, Springer, Berlin, 1984, pp. 223–244.
[1] Zvonkin, A. K.A transformation of the phase space of a diffusion process that removes the drift, Math. USSR Sbornik, 22, 129–149 1974.

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.