Ukrainian Mathematical Journal

, Volume 54, Issue 4, pp 613–628 | Cite as

On Invariant Tori of Itô Stochastic Systems

  • A. M. Samoilenko
  • A. N. Stanzhitskii


By using the Green–Samoilenko function, we establish conditions for the existence of invariant sets of Itô stochastic systems that are extensions of dynamical systems on a torus.


Dynamical System Stochastic System Samoilenko Function 
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    O. M. Stanzhyts'kyi, “Investigation of stability of invariant sets using local coordinates,” Nelin. Kolyvannya, 3, No. 2, 266–270 (2000).Google Scholar
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    I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1982).Google Scholar
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    A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian], Nauka, Moscow (1987).Google Scholar
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    E. F. Tsar'kov, Random Perturbations of Functional Differential Equations [in Russian], Zinatne, Riga (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • A. M. Samoilenko
    • 1
  • A. N. Stanzhitskii
    • 2
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKiev
  2. 2.Shevchenko Kiev National UniversityKiev

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