Skip to main content

On some open problems in constructive probability theory

  • Conference paper
  • First Online:
Constructive Mathematics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 873))

Abstract

In this paper we discuss some problems in several areas of constructive probability theory: construction of Markov processes, Martingale theory, and potential theory. We hope to convince the reader that modern probability theory is a fertile source of challenging problems for the constructivist, and that adequate tools are available for their investigation.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
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. Chan, Y.K., Notes on Constructive Probability Theory, Annals of Probability, Vol. 2, 1974.

    Google Scholar 

  2. Kurtz, T. G., Semigroups of Conditioned Shifts and Approximation of Markov Processes, Annals of Probability, Vol. 3, 1975.

    Google Scholar 

  3. Billingsley, P., "Convergence of Probability Measures," J. Wiley, N.Y., 1968.

    MATH  Google Scholar 

  4. Bishop, E., and Cheng, H., "Constructive Measure Theory," Amer. Math. Soc. Memoirs, Vol. 116, 1972.

    Google Scholar 

  5. Chung, K. L., "A Course in Probability Theory," Harcourt Brace & World, 1968.

    Google Scholar 

  6. Chan, Y. K., On Constructive Convergence of Measures on the Real Line, Annals of Probability, Vol. 2, 1974.

    Google Scholar 

  7. Heyting, A., "Intuitionism," 2nd ed. rev., North-Holland, Amsterdam, 1966.

    MATH  Google Scholar 

  8. Blumenthal, R. M., and Getoor, R., "Markov Processes and Potential Theory," Academic Press, 1968.

    Google Scholar 

  9. Lipster, R. S., and Shiryayev, A. N., "Statistics of Random Processes I," Springer-Verlag, N.Y., 1977.

    Google Scholar 

  10. McKean, H. P., Jr., "Stochastic Integral," Academic Press, 1969.

    Google Scholar 

  11. Helms, L. L., "Introduction to Potential Theory," Wiley Interscience, N.Y., 1969.

    MATH  Google Scholar 

  12. Chan, Y. K., Constructive Foundations of Potential Theory, Pacific Journal of Mathematics, Vol. 72, No. 2, 1977.

    Google Scholar 

  13. Bishop, E., "Foundations of Constructive Analysis," McGraw-Hill, N.Y., 1967.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Fred Richman

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Chan, Y.K. (1981). On some open problems in constructive probability theory. In: Richman, F. (eds) Constructive Mathematics. Lecture Notes in Mathematics, vol 873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090726

Download citation

  • DOI: https://doi.org/10.1007/BFb0090726

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10850-4

  • Online ISBN: 978-3-540-38759-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics