Skip to main content
Log in

Investigation of Invariant Sets of Itô Stochastic Systems with the Use of Lyapunov Functions

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

By using Lyapunov functions, we obtain conditions for the invariance and stochastic stability of invariant sets of Itô-type systems.

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. I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1982).

    Google Scholar 

  2. A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987); English translation: Kluwer, Dordrecht (1991).

    Google Scholar 

  3. A. M. Stanzhitskii, “Investigation of invariant sets with random perturbations with the use of Lyapunov functions,” Ukr. Mat. Zh., 50, No. 2, 309–312 (1998).

    Google Scholar 

  4. G. L. Kulinich and O. V. Pereguda, “Phase picture of the diffusion processes with the degenerate diffusion matrices,” Random Oper. Stochast. Equat., 5, No. 8, 203–216 (1997).

    Google Scholar 

  5. R. Z. Khas'minskii, Stability of Systems of Differential Equations under Random Perturbation of Their Parameters [in Russian], Nauka, Moscow (1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stanzhitskii, A.M. Investigation of Invariant Sets of Itô Stochastic Systems with the Use of Lyapunov Functions. Ukrainian Mathematical Journal 53, 323–327 (2001). https://doi.org/10.1023/A:1010437625118

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010437625118

Keywords

Navigation