Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-6bf8c574d5-h6jzd Total loading time: 0.001 Render date: 2025-02-24T04:26:34.951Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 December 2011

Ari Arapostathis ,
Vivek S. Borkar  and
Mrinal K. Ghosh
Ari Arapostathis
Affiliation:
University of Texas, Austin
Vivek S. Borkar
Affiliation:
Tata Institute of Fundamental Research, Mumbai, India
Mrinal K. Ghosh
Affiliation:
Indian Institute of Science, Bangalore
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Ergodic Control of Diffusion Processes , pp. 311 - 318
Publisher: Cambridge University Press
Print publication year: 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Agmon, S., Douglis, A., and Nirenberg, L. 1959. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Comm. Pure Appl. Math., 12, 623–727.CrossRefGoogle Scholar
[2] Allinger, D. F. and Mitter, S. K. 1980. New results on the innovations problem for nonlinear filtering. Stochastics, 4(4), 339–348.CrossRefGoogle Scholar
[3] Anderson, E. J. and Nash, P. 1987. Linear Programming in Infinite-Dimensional Spaces. Wiley-Interscience Series in Discrete Mathematics and Optimization. Chichester: John Wiley & Sons.Google Scholar
[4] Arapostathis, A. and Borkar, V. S. 2010. Uniform recurrence properties of controlled diffusions and applications to optimal control. SIAM J. Control Optim., 48(7), 152–160.CrossRefGoogle Scholar
[5] Arapostathis, A. and Ghosh, M. K. 2004 (Dec). Ergodic control of jump diffusions in ℝd under a near-monotone cost assumption. Pages 4140–4145 of:43rd IEEE Conference on Decision and Control, vol. 4.Google Scholar
[6] Arapostathis, A., Borkar, V. S., Fernández-Gaucherand, E., Ghosh, M. K., and Marcus, S. I. 1993. Discrete-time controlled Markov processes with average cost criterion: a survey. SIAM J. Control Optim., 31(2), 282–344.CrossRefGoogle Scholar
[7] Arapostathis, A., Ghosh, M. K., and Marcus, S. I. 1999. Harnack's inequality for cooperative, weakly coupled elliptic systems. Comm. Partial Differential Equations, 24, 1555–1571.CrossRefGoogle Scholar
[8] Arisawa, M., and Lions, P.-L. 1998. On ergodic stochastic control. Comm. Partial Differential Equations, 23(11–12), 333–358.CrossRefGoogle Scholar
[9] Arrow, K. J., Barankin, E. W., and Blackwell, D. 1953. Admissible points of convex sets. Pages 87–91 of: Contributions to the Theory of Games, vol. 2. Annals of Mathematics Studies, no. 28. Princeton, NJ: Princeton University Press.Google Scholar
[10] Bachelier, L. 2006. Louis Bachelier's Theory of Speculation: The Origins of Modern Finance. Princeton, NJ: Princeton University Press. Translated and with a commentary by Mark Davis and Alison Etheridge.
[11] Basak, G. K., Borkar, V. S., and Ghosh, M. K. 1997. Ergodic control of degenerate diffusions. Stochastic Anal. Appl., 15(1), 1–17.CrossRefGoogle Scholar
[12] Bass, R. F. 1998. Diffusions and Elliptic Operators. Probability and its Applications. New York: Springer-Verlag.Google Scholar
[13] Beneš, V. E. 1970. Existence of optimal strategies based on specified information, for a class of stochastic decision problems. SIAM J. Control, 8, 179–188.CrossRefGoogle Scholar
[14] Bensoussan, A. 1982. Stochastic Control by Functional Analysis Methods. Studies in Mathematics and its Applications, vol. 11. Amsterdam: North-Holland Publishing Co.Google Scholar
[15] Bensoussan, A. and Borkar, V. 1984. Ergodic control problem for one-dimensional diffusions with near-monotone cost. Systems Control Lett., 5(2), 127–133.CrossRefGoogle Scholar
[16] Bensoussan, A. and Borkar, V. 1986. Corrections to: “Ergodic control problem for onedimensional diffusions with near-monotone cost” [Systems Control Lett. 5(1984), no. 2, 127–133]. Systems Control Lett., 7(3), 233–235.CrossRefGoogle Scholar
[17] Bensoussan, A. and Frehse, J. 1992. On Bellman equations of ergodic control in Rn. J. Reine Angew. Math., 429, 125–160.Google Scholar
[18] Bensoussan, A. and Frehse, J. 2002. Ergodic control Bellman equation with Neumann boundary conditions. Pages 59–71 of: Stochastic Theory and Control (Lawrence, KS, 2001). Lecture Notes in Control and Inform. Sci., vol. 280. Berlin: Springer.Google Scholar
[19] Bertoin, J. 1996. Lévy Processes. Cambridge Tracts in Mathematics, vol. 121. Cambridge: Cambridge University Press.Google Scholar
[20] Bertsekas, D. P. and Shreve, S. E. 1978. Stochastic Optimal Control: The Discrete Time Case. New York: Academic Press.Google Scholar
[21] Bhatt, A. G. and Borkar, V. S. 1996. Occupation measures for controlled Markov processes: characterization and optimality. Ann. Probab., 24(3), 1531–1562.Google Scholar
[22] Bhatt, A. G. and Borkar, V. S. 2005. Existence of optimal Markov solutions for ergodic control of Markov processes. Sankhyā, 67(1), 1–18.Google Scholar
[23] Bhatt, A. G. and Karandikar, R. L. 1993. Invariant measures and evolution equations for Markov processes characterized via martingale problems. Ann. Probab., 21(4), 2246–2268.CrossRefGoogle Scholar
[24] Billingsley, P. 1968. Convergence of Probability Measures. New York: John Wiley & Sons.Google Scholar
[25] Billingsley, P. 1995. Probability and Measure. Third edition. Wiley Series in Probability and Mathematical Statistics. New York: John Wiley & Sons.Google Scholar
[26] Bogachev, V. I., Krylov, N. V., and Röckner, M. 2001. On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions. Comm. Partial Differential Equations, 26(11–12), 2037–2080.CrossRefGoogle Scholar
[27] Bogachev, V. I., Rökner, M., and Stannat, V. 2002. Uniqueness of solutions of elliptic equations and uniqueness of invariant measures of diffusions. Mat. Sb., 193(7), 3–36.Google Scholar
[28] Borkar, V. S. 1989a. Optimal Control of Diffusion Processes. Pitman Research Notes in Mathematics Series, vol. 203. Harlow: Longman Scientific & Technical.Google Scholar
[29] Borkar, V. S. 1989b. A topology for Markov controls. Appl. Math. Optim., 20(1), 55–62.CrossRefGoogle Scholar
[30] Borkar, V. S. 1991. On extremal solutions to stochastic control problems. Appl. Math. Optim., 24(3), 317–330.CrossRefGoogle Scholar
[31] Borkar, V. S. 1993. Controlled diffusions with constraints. II. J. Math. Anal. Appl., 176(2), 310–321.CrossRefGoogle Scholar
[32] Borkar, V. S. 1995. Probability Theory: An Advanced Course. New York: Springer-Verlag.CrossRefGoogle Scholar
[33] Borkar, V. S. 2003. Dynamic programming for ergodic control with partial observations. Stochastic Process. Appl., 103(2), 293–310.CrossRefGoogle Scholar
[34] Borkar, V. S. and Budhiraja, A. 2004a. Ergodic control for constrained diffusions: characterization using HJB equations. SIAM J. Control Optim., 43(4), 1467–1492.CrossRefGoogle Scholar
[35] Borkar, V. S. and Budhiraja, A. 2004b. A further remark on dynamic programming for partially observed Markov processes. Stochastic Process. Appl., 112(1), 79–93.CrossRefGoogle Scholar
[36] Borkar, V. S. and Gaitsgory, V. 2007. Singular perturbations in ergodic control of diffusions. SIAM J. Control Optim., 46(5), 1562–1577.CrossRefGoogle Scholar
[37] Borkar, V. S. and Ghosh, M. K. 1988. Ergodic control of multidimensional diffusions. I. The existence results. SIAM J. Control Optim., 26(1), 112–126.CrossRefGoogle Scholar
[38] Borkar, V. S. and Ghosh, M. K. 1990a. Controlled diffusions with constraints. J. Math. Anal. Appl., 152(1), 88–108.CrossRefGoogle Scholar
[39] Borkar, V. S. and Ghosh, M. K. 1990b. Ergodic control of multidimensional diffusions. II. Adaptive control. Appl. Math. Optim., 21(2), 191–220.CrossRefGoogle Scholar
[40] Borkar, V. S. and Ghosh, M. K. 2003. Ergodic control of partially degenerate diffusions in a compact domain. Stochastics, 75(4), 221–231.Google Scholar
[41] Borkar, V. S. and Mitter, S. K. 2003. A note on stochastic dissipativeness. Pages 41– 49 of: Directions in mathematical systems theory and optimization. Lecture Notes in Control and Inform. Sci., vol. 286. Berlin: Springer.CrossRefGoogle Scholar
[42] Busca, J. and Sirakov, B. 2004. Harnack type estimates for nonlinear elliptic systems and applications. Ann. Inst. H. Poincaré Anal. Non Linéaire, 21(5), 543–590.CrossRefGoogle Scholar
[43] Chen, Y.-Z. and Wu, L.-C. 1998. Second Order Elliptic Equations and Elliptic Systems. Translations of Mathematical Monographs, vol. 174. Providence, RI: American Mathematical Society. Translated from the 1991 Chinese original by Bei Hu.CrossRefGoogle Scholar
[44] Choquet, G. 1969. Lectures on Analysis. Vol. II: Representation Theory. Edited by Marsden, J., Lance, T. and Gelbart, S.. New York: W. A. Benjamin.Google Scholar
[45] Chung, K. L. 1982. Lectures from Markov Processes to BrownianMotion. Grundlehren der Mathematischen Wissenschaften, vol. 249. New York: Springer-Verlag.CrossRefGoogle Scholar
[46] Crandall, M. G., Kocan, M., and Święch, A. 2000. Lp-theory for fully nonlinear uniformly parabolic equations. Comm. Partial Differential Equations, 25(11–12), 1997–2053.
[47] Dellacherie, C. and Meyer, P. 1978. Probabilities and Potential A. North-Holland Mathematics Studies, vol. 29. Amsterdam: North-Holland.Google Scholar
[48] Dubins, L. 1962. On extreme points of convex sets. J. Math. Anal. Appl., 5, 237–244.CrossRefGoogle Scholar
[49] Dubins, L. and Freedman, D. 1964. Measurable sets of measures. Pacific J. Math., 14, 1211–1222.CrossRefGoogle Scholar
[50] Dudley, R. M. 2002. Real Analysis and Probability. Cambridge Studies in Advanced Mathematics, vol. 74. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
[51] Dunford, N. and Schwartz, J. T. 1988. Linear Operators. Part I. Wiley Classics Library. New York: John Wiley & Sons.Google Scholar
[52] Dupuis, P. and Ishii, H. 1991. On Lipschitz continuity of the solution mapping to the Skorohod problem with applications. Stochastics, 35, 31–62.Google Scholar
[53] Dynkin, E. B. and Yushkevich, A. A. 1979. Controlled Markov Processes. Grundlehren der Mathematischen Wissenschaften, vol. 235. Berlin: Springer-Verlag.
[54] El Karoui, N., Nguyen, D. H., and Jeanblanc-Picqué, M. 1987. Compactification methods in the control of degenerate diffusions: existence of an optimal control. Stochastics, 20(3), 169–219.Google Scholar
[55] Ethier, S. N. and Kurtz, T. G. 1986. Markov Processes. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. New York: John Wiley & Sons.
[56] Fabes, E. B. and Kenig, C. E. 1981. Examples of singular parabolic measures and singular transition probability densities. Duke Math. J., 48(4), 845–856.CrossRefGoogle Scholar
[57] Feller, W. 1959. Non-Markovian processes with the semigroup property. Ann. Math. Statist., 30, 1252–1253.CrossRefGoogle Scholar
[58] Fleming, W. H. and Rishel, R. W. 1975. Deterministic and Stochastic Optimal Control. Berlin: Springer-Verlag.CrossRefGoogle Scholar
[59] Fleming, W. H. 1980. Measure-valued processes in the control of partially-observable stochastic systems. Appl. Math. Optim., 6(3), 271–285.CrossRefGoogle Scholar
[60] Fleming, W. H., and Pardoux, E. 1982. Optimal control for partially observed diffusions. SIAM J. Control Optim., 20(2), 261–285.CrossRefGoogle Scholar
[61] Freidlin, M. I. 1963. Diffusion processes with reflection and a directional derivative problem on a manifold with boundary. Theory Probab. Appl., 8(1), 75–83.CrossRefGoogle Scholar
[62] Friedman, A. 1964. Partial Differential Equations of Parabolic Type. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
[63] Friedman, A. 2006. Stochastic Differential Equations and Applications. Mineola, NY: Dover Publications.Google Scholar
[64] Ghosh, M. K., Arapostathis, A., and Marcus, S. I. 1993. Optimal control of switching diffusions with application to flexible manufacturing systems. SIAM J. Control Optim., 31(5), 1183–1204.CrossRefGoogle Scholar
[65] Ghosh, M. K., Arapostathis, A., and Marcus, S. I. 1997. Ergodic control of switching diffusions. SIAM J. Control Optim., 35(6), 1952–1988.CrossRefGoogle Scholar
[66] Gikhman, I. I. and Skorokhod, A. V. 1969. Introduction to the Theory of Random Processes. Translated from the Russian by Scripta Technica, Inc. Philadelphia, PA: W. B. Saunders.Google Scholar
[67] Gilbarg, D. and Trudinger, N. S. 1983. Elliptic Partial Differential Equations of Second Order. Second edition. Grundlehren der Mathematischen Wissenschaften, vol. 224. Berlin: Springer-Verlag.CrossRefGoogle Scholar
[68] Gyöngy, I. and Krylov, N. 1996. Existence of strong solutions for Itô's stochastic equations via approximations. Probab. Theory Related Fields, 105(2), 143–158.CrossRefGoogle Scholar
[69] Has′minskiĭ, R. Z. 1960. Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations. Theory Probab. Appl., 5(2), 179–196.CrossRefGoogle Scholar
[70] Has'minskiĭ, R. Z. 1980. Stochastic Stability of Differential Equations. The Netherlands: Sijthoff & Noordhoff.CrossRefGoogle Scholar
[71] Haussmann, U. G. 1985. L'équation de Zakai et le problème séparè du contrôle optimal stochastique. Pages 37–62 of: Séminaire de Probabilités, XIX, 1983/84. Lecture Notes in Math., vol. 1123. Berlin: Springer.CrossRefGoogle Scholar
[72] Haussmann, U. G. 1986. Existence of optimal Markovian controls for degenerate diffusions. Pages 171–186 of: Stochastic Differential Systems (Bad Honnef, 1985). Lecture Notes in Control and Information Science, vol. 78. Berlin: Springer.Google Scholar
[73] Hernández-Lerma, O. 1989. Adaptive Markov Control Processes. Applied Mathematical Sciences, vol. 79. New York: Springer-Verlag.CrossRefGoogle Scholar
[74] Ikeda, N. and Watanabe, S. 1989. Stochastic Differential Equations and Diffusion Processes. Second edition. North-Holland Mathematical Library, vol. 24. Amsterdam: North-Holland Publishing.Google Scholar
[75] Kallenberg, L. C. M. 1983. Linear Programming and Finite Markovian Control Problems. Mathematical Centre Tracts, vol. 148. Amsterdam: Mathematisch Centrum.Google Scholar
[76] Karatzas, I. and Shreve, S. E. 1991. Brownian Motion and Stochastic Calculus. Second edition. Graduate Texts in Mathematics, vol. 113. New York: Springer-Verlag.Google Scholar
[77] Kogan, Ya. A. 1969. The optimal control of a non-stopping diffusion process with reflection. Theory Probab. Appl., 14(3), 496–502.CrossRefGoogle Scholar
[78] Krylov, N. V. 1980. Controlled Diffusion Processes. Applications of Mathematics, vol. 14. New York: Springer-Verlag. Translated from the Russian by A. B. Aries.CrossRefGoogle Scholar
[79] Krylov, N. V. 1995. Introduction to the Theory of Diffusion Processes. Translations of Mathematical Monographs, vol. 142. Providence, RI: American Mathematical Society.Google Scholar
[80] Kunita, H. 1981. Some extensions of Itô's formula. Pages 118–141 of: Seminar on Probability, XV (Univ. Strasbourg, Strasbourg, 1979/1980) (French). Lecture Notes in Math., vol. 850. Berlin: Springer.Google Scholar
[81] Kurtz, T. G. and Stockbridge, R. H. 1998. Existence of Markov controls and characterization of optimal Markov controls. SIAM J. Control Optim., 36(2), 609–653.CrossRefGoogle Scholar
[82] Kurtz, T. G. and Stockbridge, R. H. 2001. Stationary solutions and forward equations for controlled and singular martingale problems. Electron. J. Probab., 6, no. 17, 52 pp. (electronic).CrossRefGoogle Scholar
[83] Ladyženskaja, O. A., Solonnikov, V. A., and Ural′ceva, N. N. 1967. Linear and Quasilinear Equations of Parabolic Type. Translated from the Russian by Smith, S.. Translations of Mathematical Monographs, Vol. 23. Providence, RI: American Mathematical Society.Google Scholar
[84] Lions, P.-L. 1983a. Optimal control of diffusion processes and Hamilton–Jacobi–Bellman equations. I. The dynamic programming principle and applications. Comm. Partial Differential Equations, 8(10), 1101–1174.CrossRefGoogle Scholar
[85] Lions, P.-L. 1983b. Optimal control of diffusion processes and Hamilton–Jacobi–Bellman equations. II. Viscosity solutions and uniqueness. Comm. Partial Differential Equations, 8(11), 1229–1276.CrossRefGoogle Scholar
[86] Lions, P. L. and Sznitman, A. S. 1984. Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math., 37, 511–537.CrossRefGoogle Scholar
[87] Liptser, R. S. and Shiryayev, A. N. 1977. Statistics of Random Processes. I. Applications of Mathematics, Vol. 5. New York: Springer-Verlag. Translated by A. B. Aries.CrossRefGoogle Scholar
[88] Luenberger, D. G. 1967. Optimization by Vector Space Methods. New York: John Wiley & Sons.Google Scholar
[89] Menaldi, J.-L. and Robin, M. 1997. Ergodic control of reflected diffusions with jumps. Appl. Math. Optim., 35(2), 117–137.CrossRefGoogle Scholar
[90] Menaldi, J.-L. and Robin, M. 1999. On optimal ergodic control of diffusions with jumps. Pages 439–456 of: Stochastic Analysis, Control, Optimization and Applications. Systems Control Found. Appl. Boston, MA: Birkhäuser Boston.CrossRefGoogle Scholar
[91] Meyn, S. and Tweedie, R. L. 2009. Markov Chains and Stochastic Stability. Second edition. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
[92] Nadirashvili, N. 1997. Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 24(3), 537–549.Google Scholar
[93] Neveu, J. 1965. Mathematical Foundations of the Calculus of Probability. San Francisco, CA: Holden-Day.Google Scholar
[94] Parthasarathy, K. R. 1967. Probability Measures on Metric Spaces. Probability and Mathematical Statistics, No. 3. New York: Academic Press.CrossRefGoogle Scholar
[95] Phelps, R. 1966. Lectures on Choquet's Theorem. New York: Van Nostrand.Google Scholar
[96] Portenko, N. I. 1990. Generalized Diffusion Processes. Translations of Mathematical Monographs, vol. 83. Providence, RI: American Mathematical Society. Translated from the Russian by H. H. McFaden.CrossRefGoogle Scholar
[97] Puterman, M. I. 1994. Markov Decision Processes: Discrete Stochastic Dynamic Programming. Hoboken, NJ: John Wiley & Sons.CrossRefGoogle Scholar
[98] Rachev, S. T. 1991. Probability Metrics and the Stability of Stochastic Models. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. Chichester: John Wiley & Sons.Google Scholar
[99] Rishel, R. 1970. Necessary and sufficient dynamic programming conditions for continuous time stochastic control problem. SIAM J. Control, 8, 559–571.CrossRefGoogle Scholar
[100] Robin, M. 1983. Long-term average cost control problems for continuous time Markov processes: a survey. Acta Appl. Math., 1(3), 281–299.CrossRefGoogle Scholar
[101] Rockafellar, R. T. 1946. Convex Analysis. Princeton Mathematical Series, vol. 28. Princeton, NJ: Princeton University Press.Google Scholar
[102] Rogers, L. C. G., and Williams, D. 2000a. Diffusions, Markov Processes, and Martingales. Vol. 1. Cambridge Mathematical Library. Cambridge: Cambridge University Press.Google Scholar
[103] Rogers, L. C. G. and Williams, D. 2000b. Diffusions, Markov Processes, and Martingales. Vol. 2. Cambridge Mathematical Library. Cambridge: Cambridge University Press.Google Scholar
[104] Ross, S. M. 1970. Average cost semi-Markov decision processes. J. Appl. Probability, 7, 649–656.CrossRefGoogle Scholar
[105] Rudin, W. 1973. Functional Analysis. New York: McGraw-Hill.Google Scholar
[106] Rugh, W. J. 1996. Linear System Theory. Second edition. Prentice Hall Information and System Sciences Series. Englewood Cliffs, NJ: Prentice Hall.Google Scholar
[107] Safonov, M. V. 1999. Nonuniqueness for second-order elliptic equations with measurable coefficients. SIAM J. Math. Anal., 30(4), 879–895 (electronic).CrossRefGoogle Scholar
[108] Skorohod, A. V. 1989. Asymptotic Methods in the Theory of Stochastic Differential Equations. Translations of Mathematical Monographs, vol. 78. Providence, RI: American Mathematical Society.Google Scholar
[109] Stannat, W. 1999. (Nonsymmetric) Dirichlet operators on L1: existence, uniqueness and associated Markov processes. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 28(1), 99–140.Google Scholar
[110] Stockbridge, R. H. 1989. Time-average control of martingale problems: the Hamilton–Jacobi–Bellman equation. Stochastics Stochastics Rep., 27(4), 249–260.CrossRefGoogle Scholar
[111] Stockbridge, R. H. 1990a. Time-average control of martingale problems: a linear programming formulation. Ann. Probab., 18(1), 206–217.CrossRefGoogle Scholar
[112] Stockbridge, R. H. 1990b. Time-average control of martingale problems: existence of a stationary solution. Ann. Probab., 18(1), 190–205.CrossRefGoogle Scholar
[113] Striebel, C. 1984. Martingale methods for the optimal control of continuous time stochastic systems. Stoch. Process. Appl., 18, 324–347.CrossRefGoogle Scholar
[114] Stroock, D. W. and Varadhan, S. R. S. 1971. Diffusion processes with boundary conditions. Comm. Pure Appl. Math., 24, 147–225.CrossRefGoogle Scholar
[115] Stroock, D. W. and Varadhan, S. R. S. 1979. Multidimensional Diffusion Processes. Grundlehren der Mathematischen Wissenschaften, vol. 233. Berlin: Springer-Verlag.Google Scholar
[116] Veretennikov, A. Yu. 1980. Strong solutions and explicit formulas for solutions of stochastic integral equations. Mat. Sb. (N.S.), 111(153)(3), 434–452, 480.Google Scholar
[117] Veretennikov, A. Yu. 1987. On strong solutions of stochastic Itô equations with jumps. Theory Probab. Appl., 32(1), 148–152.CrossRefGoogle Scholar
[118] Wagner, D. H. 1977. Survey of measurable selection theorems. SIAM J. Control Optim., 15, 859–903.CrossRefGoogle Scholar
[119] Walters, P. 1982. An Introduction to Ergodic Theory. Graduate Texts in Mathematics, vol. 79. New York: Springer-Verlag.CrossRefGoogle Scholar
[120] Willems, J. C. 1972. Dissipative dynamical systems. I. General theory. Arch. Rational Mech. Anal., 45, 321–351.CrossRefGoogle Scholar
[121] Wong, E. 1971. Representation of martingales, quadratic variation and applications. SIAM J. Control, 9, 621–633.CrossRefGoogle Scholar
[122] Wong, E. and Hajek, B. 1985. Stochastic Processes in Engineering Systems. Springer Texts in Electrical Engineering. New York: Springer-Verlag.CrossRefGoogle Scholar
[123] Wu, W., Arapostathis, A., and Shakkottai, S. 2006. Optimal power allocation for a timevarying wireless channel under heavy-traffic approximation. IEEE Trans. Automat. Control, 51(4), 580–594.CrossRefGoogle Scholar
[124] Xiong, J. 2008. An Introduction to Stochastic Filtering Theory. Oxford Graduate Texts in Mathematics, vol. 18. Oxford: Oxford University Press.Google Scholar
[125] Yosida, K. 1980. Functional Analysis. Sixth edition. Grundlehren der Mathematischen Wissenschaften, vol. 123. Berlin: Springer-Verlag.Google Scholar
[126] Young, L. C. 1969. Lectures on the Calculus of Variations and Optimal Control Theory. Foreword by Wendell Fleming, H.. Philadelphia: W. B. Saunders.Google Scholar
[127] Zvonkin, A. K. 1974. A transformation of the phase space of a diffusion process that will remove the drift. Mat. Sb. (N.S.), 93(135), 129–149, 152.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Ari Arapostathis, University of Texas, Austin, Vivek S. Borkar, Tata Institute of Fundamental Research, Mumbai, India, Mrinal K. Ghosh, Indian Institute of Science, Bangalore
  • Book: Ergodic Control of Diffusion Processes
  • Online publication: 05 December 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9781139003605.013
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Ari Arapostathis, University of Texas, Austin, Vivek S. Borkar, Tata Institute of Fundamental Research, Mumbai, India, Mrinal K. Ghosh, Indian Institute of Science, Bangalore
  • Book: Ergodic Control of Diffusion Processes
  • Online publication: 05 December 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9781139003605.013
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Ari Arapostathis, University of Texas, Austin, Vivek S. Borkar, Tata Institute of Fundamental Research, Mumbai, India, Mrinal K. Ghosh, Indian Institute of Science, Bangalore
  • Book: Ergodic Control of Diffusion Processes
  • Online publication: 05 December 2011
  • Chapter DOI: https://doi.org/10.1017/CBO9781139003605.013
Available formats
×