Skip to main content
Log in

On Stability of Solutions of a Stochastic Equation

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We present conditions for the stability of stationary solutions of an abstract linear stochastic differential equation with respect to the coefficient of the leading derivative.

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. A. N. Shiryaev, Probability [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  2. V. M. Kruglov, Additional Chapters of Probability Theory [in Russian], Vysshaya Shkola, Moscow (1984).

    Google Scholar 

  3. A. Ya. Dorogovtsev, “Stability of stationary solutions,” Dokl. Ros. Akad. Nauk, 369, No. 3, 309–310 (1999).

    Google Scholar 

  4. R. F. Curtain and P. L. Falb, “Stochastic differential equation in Hilbert space,” J. Different. Equat., 10, No. 3, 412–430 (1971).

    Google Scholar 

  5. A. Ya. Dorogovtsev, Periodic and Stationary Modes of Infinite-Dimensional Deterministic and Stochastic Dynamical Systems [in Russian], Vyshcha Shkola, Kiev (1992).

    Google Scholar 

  6. V. I. Bogachev, Gaussian Measures [in Russian], Nauka, Moscow (1997).

    Google Scholar 

  7. M. Sh. Birman and M. Z. Solomyak, Spectral Theory of Self-Adjoint Operators in a Hilbert Space [in Russian], Leningrad University, Leningrad (1980).

    Google Scholar 

  8. A. Ya. Dorogovtsev, “Stationary and periodic solutions of stochastic difference and differential equations in Banach space,” in: V. V. Sasonov and T. Shervashidze (editors), New Trends in Probability and Statistics (Proceedings of the Bakuriani Colloquium in Honor of Yu. V. Prohorov), Vol. 1, Mokslas, Vilnius (1991), pp. 375–390.

    Google Scholar 

  9. D. Henry, Geometric Theory of Semilinear Parabolic Equations [Russian translation], Mir, Moscow (1985).

    Google Scholar 

  10. T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin (1966).

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dorogovtsev, A.Y. On Stability of Solutions of a Stochastic Equation. Ukrainian Mathematical Journal 56, 22–36 (2004). https://doi.org/10.1023/B:UKMA.0000031701.23961.e9

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:UKMA.0000031701.23961.e9

Keywords

Navigation