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Averaging for partial differential equations whose coefficients are perturbed by jump-like Markov processes

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Abstract

Weak convergence in the sense of distributions of the solutions of parabolic-type partial differential equations with periodic rapidly oscillating coefficients perturbed by jump-like Markov processes that function in “rapid” time with finite state set is considered. The weak compactness of the measures generated by the solutions of the equations is proved and the weak convergence to a unique solution of the Martingale problem that satisfies a stochastic partial differential equation is demonstrated.

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Authors and Affiliations

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

    Yu. V. Kolomiyets'

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  1. Yu. V. Kolomiyets'
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1367–1375, October, 1992.

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Kolomiyets', Y.V. Averaging for partial differential equations whose coefficients are perturbed by jump-like Markov processes. Ukr Math J 44, 1253–1261 (1992). https://doi.org/10.1007/BF01057682

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  • DOI: https://doi.org/10.1007/BF01057682

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