Skip to main content
SpringerLink
Log in

Completeness theorems for the general theory of stochastic processes

  • Conference paper
  • First Online:
Methods in Mathematical Logic

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1130))

I wish to thank my advisor, Professor H.J. Keisler for suggesting the subject of this paper and for his invaluable comments. This research was partially supported by a University of Wisconsin Research Assistantship.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, R.M., A non-standard Representation of Brownian Motion and Itô Integration, Israel J.Math 25(1976), pp. 15–46.

    Article  MathSciNet  MATH  Google Scholar 

  2. Ash, R., Real Analysis and Probability, Academic Press (1972)

    Google Scholar 

  3. Cutland, N., On the Existence of Strong Solutions to Stochastic Differential Equations on Loeb Spaces, Z.W.V.G., 60(1982), pp. 335–357.

    MathSciNet  MATH  Google Scholar 

  4. Dellacherie, C., Capacites et Processus Stochastiques, Springer-Verlag, (1972).

    Google Scholar 

  5. Dellacherie, C. and Meyer, P.A., Probabilities and Potential, Vol. I, North-Holland, 1978.

    Google Scholar 

  6. _____, Probabilités et Potentiel, Vol. II, Hermann, 1980.

    Google Scholar 

  7. Elliot, R., Stochastic Calculus and its Applications, Springer-Verlag, (1982).

    Google Scholar 

  8. Fajardo, S., Probability Logic with Conditional Expectation in: Annals of pure and applied Logics (To appear).

    Google Scholar 

  9. Hoover, D., Probability Logic, Ph.D. Thesis, Univ. of Wisconsin (1978)

    Google Scholar 

  10. _____, Probability Logic, Ann.Math.Logic 14 (1978), pp. 287–313.

    Article  MathSciNet  MATH  Google Scholar 

  11. _____, A Normal Form Theorem for Lw,p with Applications, J.S.L. 47(1982), pp. 605–624.

    MathSciNet  MATH  Google Scholar 

  12. _____, A Probabilistic Interpolation Theorem. (To appear)

    Google Scholar 

  13. Hoover, D. and Keisler, H.J., Adapted Probability Distributions. T.A.M.S. (To appear).

    Google Scholar 

  14. Hoover, D. and Perkins, E., Nonstandard Construction of the Stochastic Integral and Applications to SDE’s. I and II, T.A.M.S. 275(1983), pp. 1–36 and 37–58.

    MathSciNet  MATH  Google Scholar 

  15. Keisler, H.J., An Infinitesimal Approach to Stochastic Analysis. Memoirs Amer.Math.Soc. 297, Vol. 48(1984).

    Google Scholar 

  16. Keisler, H.J., Hyperfinite Probability Theory and Probability Logic. Lecture Notes, Univ. of Wisconsin (Unpublished) (1982).

    Google Scholar 

  17. _____, Probability Quantifiers, To appear in Abstract Model Theory and Logics of Mathematical Concepts, ed. by J. Barwise and F. Feferman, Springer-Verlag.

    Google Scholar 

  18. _____, Hyperfinite Model Theory, pp. 5–110 in Logic Colloquium 76, North-Holland (1977).

    Google Scholar 

  19. _____, A Completeness Proof for Adapted Probability Logic. (To appear)

    Google Scholar 

  20. Lindström, T., Hyperfinite Stochastic Integration, I, II, and III. Math.Scand. 46(1980), pp 265–333.

    MathSciNet  MATH  Google Scholar 

  21. Loeb, P., Conversion from Nonstandard to Standard Measure Space and Applications to Probability Theory, T.A.M.S. 211(1975), pp. 113–122.

    Article  MathSciNet  MATH  Google Scholar 

  22. Metiver, M. and Pellaumail, J., Stochastic Integration, Academic Press, 1980.

    Google Scholar 

  23. Panetta, L., Hyperreal Probability Spaces: Some Applications of the Loeb Construction, Ph.D. Thesis, Univ. of Wisconsin (1978)

    Google Scholar 

  24. Perkins, E., Stochastic Processes and Nonstandard Analysis. LNM 983.

    Google Scholar 

  25. Rodenhausen, H., The Completeness Theorem for Adapted Probability Logic, Ph.D. Thesis, Heidelberg University (1982).

    Google Scholar 

  26. Skorokhod, A.V., On Measurability of Stochastic Processes, Theory of Probability and Its Applications, Vol. XXV,(1980), pp.139–141.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Author notes

  1. Sergio Fajardo

    Present address: Department of Mathematics, University of Colorado, Campus Box 426, 80309, Boulder, Colorado, USA

Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, 53706, Madison, Wisconsin, USA

    Sergio Fajardo

Authors
  1. Sergio Fajardo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Carlos Augusto Di Prisco

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Fajardo, S. (1985). Completeness theorems for the general theory of stochastic processes. In: Di Prisco, C.A. (eds) Methods in Mathematical Logic. Lecture Notes in Mathematics, vol 1130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075311

Download citation

  • DOI: https://doi.org/10.1007/BFb0075311

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15236-1

  • Online ISBN: 978-3-540-39414-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation