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Averaging of randomly perturbed evolutionary equations

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Abstract

Evolutionary equations with coefficients perturbed by diffusion processes are considered. It is proved that the solutions of these equations converge weakly in distribution, as a small parameter tends to zero, to a unique solution of a martingale problem that corresponds to an evolutionary stochastic equation in the case where the powers of a small parameter are inconsistent.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    Yu. V. Kolomiets

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  1. Yu. V. Kolomiets
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 963–971, July, 1993.

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Kolomiets, Y.V. Averaging of randomly perturbed evolutionary equations. Ukr Math J 45, 1066–1076 (1993). https://doi.org/10.1007/BF01057453

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  • DOI: https://doi.org/10.1007/BF01057453

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