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Ukrainian Mathematical Journal

, Volume 57, Issue 7, pp 1035–1054 | Cite as

A Stochastic Analog of Bogolyubov's Second Theorem

  • B. V. Bondarev
  • E. E. Kovtun
Article
  • 21 Downloads

Abstract

We establish an estimate for the rate at which a solution of an ordinary differential equation subject to the action of an ergodic random process converges to a stationary solution of a deterministic averaged system on time intervals of order \(e^{1/\varepsilon ^\rho }\) for some 0 < ρ < 1.

Keywords

Differential Equation Ordinary Differential Equation Stationary Solution Random Process Stochastic Analog 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • B. V. Bondarev
    • 1
  • E. E. Kovtun
    • 1
  1. 1.Donetsk National UniversityDonetskUkraine

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