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Averagings in stochastic systems with dependence on the whole past

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Abstract

The averaging principle is justified for stochastic systems, subjected to weakly dependent random actions. For normalized fluctuations of the solutions of the initial equation with respect to the solution of the averaged equation, one constructs exponential estimates of the type of Bernshtein's inequalities of sums of independent random variables.

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Authors and Affiliations

  1. Donetsk University, USSR

    B. V. Bondarev

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  1. B. V. Bondarev
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 443–451, April, 1990.

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Bondarev, B.V. Averagings in stochastic systems with dependence on the whole past. Ukr Math J 42, 391–397 (1990). https://doi.org/10.1007/BF01071323

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  • DOI: https://doi.org/10.1007/BF01071323

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