Skip to main content
Log in

Smoothing Problem in Anticipating Scenario

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We consider a smoothing problem for stochastic processes satisfying stochastic differential equations with Wiener processes that may not have a semimartingale property with respect to the joint filtration.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. K. Ito and H. P. McKean, Jr., “Diffusion processes and their sample paths. Second printing, corrected,” in: Grundlehren Math. Wissenschaften, Springer, Berlin-New York (1974).

    Google Scholar 

  2. B. Simon, The P(φ) 2 Euclidean (Quantum) Field Theory, Princeton Univ. Press (1974).

  3. A. A. Dorogovtsev, Stochastic Analysis and Random Maps in Hilbert Space, VSP, Utrecht-Tokyo (1994).

    Google Scholar 

  4. A. A. Dorogovtsev, “Anticipating equations and filtration problem,” Theory Stochast. Processes, 3(19), Issue 1–2, 154–163 (1997).

    MATH  Google Scholar 

  5. A. A. Dorogovtsev, “Conditional measures for diffusion processes and anticipating stochastic equations, ” Theory Stochast. Processes, 4(20), 17–24 (1998).

    MATH  MathSciNet  Google Scholar 

  6. A. V. Skorokhod, “One generalization of the stochastic integral,” Probab. Theory Its Appl., 20, No.2, 223–237 (1975).

    MATH  Google Scholar 

  7. R. Sh. Liptser and A. N. Shyriaev, Statistics of Random Processes [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  8. P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).

    Google Scholar 

  9. B. B. Mandelbrot and J. van Ness, “Fractional Brownian motion, fractional noises and applications, ” SIAM Rev., 10, 422–437 (1968).

    Article  MathSciNet  Google Scholar 

  10. S. Tindel, C. A. Tudor, and F. Viens, “Stochastic evolution equations with fractional Brownian motion, ” Probab. Theory Relat. Fields, 127, No.2, 186–204 (2003).

    Article  MathSciNet  Google Scholar 

  11. A. A. Dorogovtsev, “An action of Gaussian strong random operator on random elements,” Probab. Theory Its Appl., 31, No.4, 811–814 (1986).

    MATH  MathSciNet  Google Scholar 

  12. P. Malliavin, “Stochastic analysis,” Text. Monograph, Grundlehren Math. Wissenschaften, 313, Springer, Berlin (1997).

    Google Scholar 

  13. D. Nualart, “The Malliavin calculus and related topics,” Text. Monograph, Probability and its Application, Springer, New York (1995).

    Google Scholar 

  14. A. A. Dorogovtsev, “Stochastic integration and one class of Gaussian stochastic processes,” Ukr. Mat. Zh., 50, No.4, 495–505 (1998).

    MATH  MathSciNet  Google Scholar 

  15. A. S. Ustunel and M. Zakai, Transformation of Measure on Wiener Space, Springer (2000).

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 9, pp. 1218–1234, September, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dorogovtsev, A.A. Smoothing Problem in Anticipating Scenario. Ukr Math J 57, 1424–1441 (2005). https://doi.org/10.1007/s11253-006-0005-9

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-006-0005-9

Keywords

Navigation