Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-09T16:22:41.077Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  30 March 2017

Sergio Fajardo
Affiliation:
Universidad de los Andes, Colombia
H. Jerome Keisler
Affiliation:
University of Wisconsin, Madison
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2002

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

S., Albeverio, J., Fenstad, R., Hoegh-Krohn, and T., Lindstrøm [1986] Nonstandard methods in stochastic analysis and mathematical physics, Academic Press.
David, Aldous [1981] Weak convergence and the general theory of processes, preprint.
Robert, Anderson [1976] A nonstandard representation for brownian motion and itˆo integration, Israel Journal of Mathematics, vol. 25, pp. 15–46.Google Scholar
Robert, Ash [1972] Real analysis and probability, Academic Press.
Martin, Barlow and Edward, Perkins [1989] Sample path properties of stochastic integrals and stochastic differentiation, Stochastics and Stochastic reports, vol. 27, pp. 261–293.Google Scholar
Martin, Barlow and Edward, Perkins[1990] On pathwise uniqueness and expansion of filtrations, Seminaire de probabilities xxvi (A., Azema et. al, editor), Lecture Notes in Mathemtics, no. 1426, Springer-Verlag, pp. 194–209.
Patrick Billingsley [1979] Probability and measure,Wiley.
C.C., Chang and H., Jerome Keisler [1990] Model theory, third edition, North Holland.
Nigel, Cutland [1983] Nonstandard measure theory and its applications, Bulletin of the London Mathematical Society, vol. 15, pp. 529–589.Google Scholar
Robert, Dalang [1989] Optimal stopping of two parameter processes on nonstandard probability spaces, Transactions of the American Mathematical Society, vol. 373, pp. 697–719.Google Scholar
Claude, Dellacherie and Paul A., Meyer [1978] Probabilities and potential, North-Holland.
Claude, Dellacherie and Paul A., Meyer[1988] Probabilities and potential c, North-Holland.
R., Durrett [1984] Brownian motion and martingales in analysis, Wadsworth.
Steve, Ethier and Tom, Kurtz [1986] Markov processes, Wiley.
Sergio, Fajardo [1985a] Completeness theorems for the general theory of processes, Methods in mathematical logic (Carlos DiPrisco, editor), Lecture Notes in Mathematics, no. 1130, Springer-Verlag, pp. 174–194.
Sergio, Fajardo[1985b] Probability logic with conditional expectation, Annals of Pure and Applied Logic, vol. 28, pp. 137–161.Google Scholar
Sergio, Fajardo[1987] Intrinsic stochastic processes, Revista Colombiana de Matemáticas, vol. 21, pp. 317–336.Google Scholar
Sergio, Fajardo[1990a] Elementary embeddings and games in adapted probability logic, Archive for Mathematical Logic, pp. 49–58.Google Scholar
Sergio, Fajardo[1990b] Introducción al análisis no-estándar y sus aplicaciones en probabilidad, Cuadernos de Probabilidad y Estadistica Matemática, no. 3, Fondo Editorial Acta Cientifica Venezolana, Caracas.
Sergio, Fajardo and H., Jerome Keisler[1995] Long sequences and neocompact sets, Developments in nonstandard analysis (Nigel, Cutland et al., editor), Longman, pp. 251–260.Google Scholar
Sergio, Fajardo and H., Jerome Keisler[1996a] Existence theorems in probability theory, Advances in Mathematics, vol. 120, pp. 191–257.Google Scholar
Sergio, Fajardo and H., Jerome Keisler[1996bSergio, Fajardo and H., Jerome Keisler] Neometric spaces, Advances in Mathematics, vol. 118, pp. 134–175.
Sergio, Fajardo and H., Jerome Keisler[1997] Games on probability spaces, preprint.
David, Fremlin[1989] Measure algebra, The handbook of boolean algebra, volume 3 (J.D.Monk and R. Bonnet, editors), North-Holland.
C., Ward Henson and H., Jerome Keisler [1986] On the strength of nonstandard analysis, The Journal of Symbolic Logic, vol. 51, pp. 377–386.Google Scholar
Wilfrid, Hodges [1985] Building models by games, Student Texts 2 , London Mathematical Society.
Douglas, Hoover [1984] Synonymity, generalized martingales and subfiltrations, Annals of Probability, vol. 12, pp. 703–713.Google Scholar
Douglas, Hoover[1987] A characterization of adapted distribution, Annals of Probability, vol. 15, pp. 1600–1611.Google Scholar
Douglas, Hoover[1990] Enlarging saturated filtrations, preprint.
Douglas, Hoover[1991] Convergence in distribution and skorokhod convergence for the general theory of processes, Probability Theory and Related Fields, vol. 89, pp. 239–259.Google Scholar
Douglas, Hoover[1992] Extending probability spaces and adapted distributions, Seminaire de probabilites xxvi (J. Azema et al., editor), Lecture Notes in Mathematics, Springer-Verlag, pp. 560–574.
Douglas, Hoover and H., Jerome Keisler [1984] Adapted probability distributions, Transactions of the American Mathematical Society, vol. 286, pp. 159–201.Google Scholar
Jean, Jacod [1979] Calcul stochastique et problémes de martingales, Lecture Notes in Mathematics, vol. 714, Springer-Verlag.
Renling, Jin and H., Jerome Keisler [2000] Maharam spectra of loeb spaces, The Journal of Symbolic Logic, vol. 65, pp. 550–566.Google Scholar
H., Jerome Keisler [1977] Hyperfinite model theory, Logic colloquium 76 (R. Gandy and J.M.E.Hyland, editors), North-Holland, pp. 5–110.
H., Jerome Keisler[1979] Hyperfinite probability theory and probability logic, Seminar notes. University ofWisconsin-Madison.
H., Jerome Keisler[1984] An infinitesimal approach to stochastic analysis,AmericanMathematical Society Memoirs, vol. 397.Google Scholar
H., Jerome Keisler[1985] Probability quantifiers, Model theoretic logics (Jon Barwise Solomon, Feferman, editor), Springer-Verlag, pp. 509–556.
H., Jerome Keisler[1986a] A completeness proof for adapted probability logic, Annals of Pure and Applied Logic, vol. 31, pp. 61–70.Google Scholar
H., Jerome Keisler[1986b] Hyperfinite models of adapted probability logic, Annals of Pure and Applied Logic, vol. 31, pp. 71–86.Google Scholar
H., Jerome Keisler[1988] Infinitesimals in probability theory, Nonstandard analysis and its applications (Nigel, Cutland, editor), LSMGT, no. 10, Cambridge University Press, pp. 106–139.
H., Jerome Keisler[1991] From discrete to continuous time, Annals of Pure and Applied Logic, vol. 52, pp. 99–141.Google Scholar
H., Jerome Keisler[1994] The hyperreal line, Real numbers, generalizations of the reals, and theories of continua (P., Erlich, editor), Kluwer, pp. 207–237.
H., Jerome Keisler[1995] A neometric survey, Developments in nonstandard analysis (Nigel, Cutland et al., editor), Longman, pp. 233–250.
H., Jerome Keisler[1997a] Rich and saturated adapted spaces, Advances in Mathematics, vol. 128, pp. 242–288.Google Scholar
H., Jerome Keisler[1997b] Solution of stochastic differential equations with extra properties, Nonstandard analysis, theory and applications (L., Arkeryd et al., editor), NATO Advanced Studies Institute, Kluwer, pp. 259–278.
H., Jerome Keisler[1998] Quantifier elimination for neocompact sets, The Journal of Symbolic Logic, vol. 63, pp. 1442–1472.Google Scholar
H., Jerome Keisler and Yeneng, Sun [2001] Loeb measures and borel algebras, Reuniting the antipodes—constructive and nonstandard views of the continuum. proceedings of the symposion in san servolo/ venice, italy, may 17-22, 1999 (H., Osswald and P., Schuster, editors), Kluwer.
Frank, Knight [1975] A predictive view of continuous time processes, Annals of Probability, vol. 3, pp. 573–596.Google Scholar
John, Lamperti [1977] Stochastic processes, Applied Mathematical Sciences, vol. 23, Springer-Verlag.
Tom, Lindstrøm [1988] An invitation to nonstandard analysis, Nonstandard analysis an its applications (Nigel, Cutland, editor), London Mathematical Society Student Texts, no. 10, Cambridge University Press, pp. 1–105.
Peter, Loeb [1975] Conversion from standard to nonstandardmeasure spaces and applications in probability theory, Transactions of the American Mathematical Society, vol. 211, pp. 113–122.Google Scholar
Paul, Loève [1977-1978] Probability theory, Springer-Verlag.
Miguel, López [1989] Distribuciones adaptadas en probabilidad. undergraduate thesis, department of mathematics, Master's thesis, Universidad de Los Andes. Bogotá. Colombia.
Dorothy, Maharam [1942] On homogeneous measure algebras, Proceedings of the National Academy of Sciences of the U.S.A., vol. 28, pp. 108–111.Google Scholar
Dorothy, Maharam[1950] Decompositions of measure algebras and spaces, Transactions of the American Mathematical Society, vol. 69, pp. 143–160.Google Scholar
Dorothy, Maharam[1958] Automorphisms of products of measure spaces, Proceedings of the American Mathematical Society, vol. 9, pp. 702–707.Google Scholar
Javier Pe, na [1993] Games between stochastic processes and a universality theorem for twoparameter stochastic processes, Master's thesis, Universidad de Los Andes. Bogot á, Colombia.
Miodrag, Raškovic and Radosav, Dordevic [1996] Probability quantifiers and operators, Vesta-Belgrade.
Emilio, Remolina [1993] Some topics in model theory of stochastic processes, Master's thesis, Universidad de Los Andes. Bogotá, Colombia.
Keith, Stroyan and José, Bayod [1986] Foundations of infinitesimal stochastic analysis, Studies in Logic and the Foundations of Mathematics, vol. 119, North-Holland.
David, Williams [1991] Probability with martingales, Cambridge Mathematical Textbooks, Cambridge University Press.

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
  • Sergio Fajardo, Universidad de los Andes, Colombia, H. Jerome Keisler, University of Wisconsin, Madison
  • Book: Model Theory of Stochastic Processes
  • Online publication: 30 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316756126.011
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
  • Sergio Fajardo, Universidad de los Andes, Colombia, H. Jerome Keisler, University of Wisconsin, Madison
  • Book: Model Theory of Stochastic Processes
  • Online publication: 30 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316756126.011
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
  • Sergio Fajardo, Universidad de los Andes, Colombia, H. Jerome Keisler, University of Wisconsin, Madison
  • Book: Model Theory of Stochastic Processes
  • Online publication: 30 March 2017
  • Chapter DOI: https://doi.org/10.1017/9781316756126.011
Available formats
×