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Ukrainian Mathematical Journal

, Volume 58, Issue 10, pp 1552–1569 | Cite as

Asymptotic equivalence of solutions of linear Itô stochastic systems

  • A. P. Krenevych
Article

Abstract

We investigate the problem of the asymptotic equivalence of stochastic systems of linear ordinary equations and stochastic equations in the sense of mean square and with probability one.

Keywords

Ordinary Differential Equation Stochastic Differential Equation Strong Solution Stochastic System Functional Differential Equation 
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References

  1. 1.
    L. Arnold, “Anticipative problems in the theory of random dynamical system in stochastic analysis,” Proc. Symp. Pure Math., 57, 529–541 (1995).Google Scholar
  2. 2.
    L. Arnold, O. Oeljeklaus, and E. Pardoux, “Almost sure and moment stability for linear Itô equations,” in: L. Arnold and V. Wihstutz (editors), Lyapunov Exponents, Springer, Berlin (1986), pp. 129–159.CrossRefGoogle Scholar
  3. 3.
    E. F. Tsar’kov, Random Perturbations of Functional Differential Equations [in Russian], Zinatne, Riga (1989).zbMATHGoogle Scholar
  4. 4.
    R. Z. Khas’minskii, Stability of Systems of Differential Equations under Random Perturbations of Their Parameters [in Russian], Nauka, Moscow (1969).Google Scholar
  5. 5.
    V. K. Yasinskii, Stochastic Functional Differential Equations with Prehistory [in Russian], TViMS, Kiev (2003).Google Scholar
  6. 6.
    V. P. Demidovich, Lectures on Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).Google Scholar
  7. 7.
    V. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1968).Google Scholar
  8. 8.
    A. A. Borovkov, A Course in Probability Theory [in Russian], Nauka, Moscow (1972).Google Scholar
  9. 9.
    V. S. Korolyuk and V. K. Yasyns’kyi, A Course in the Theory of Probability, Random Processes, and Mathematical Statistics [in Ukrainian], Zoloti Lytavry, Chernivtsi (2005).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. P. Krenevych
    • 1
  1. 1.Shevchenko Kyiv National UniversityKyiv

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