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A Stochastic Analog of Bogolyubov's Second Theorem

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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.

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Authors and Affiliations

  1. Donetsk National University, Donetsk, Ukraine

    B. V. Bondarev & E. E. Kovtun

Authors
  1. B. V. Bondarev
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  2. E. E. Kovtun
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 879–894, July, 2005.

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Bondarev, B.V., Kovtun, E.E. A Stochastic Analog of Bogolyubov's Second Theorem. Ukr Math J 57, 1035–1054 (2005). https://doi.org/10.1007/s11253-005-0246-z

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  • DOI: https://doi.org/10.1007/s11253-005-0246-z

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