An averaging principle for slow–fast fractional stochastic parabolic equations on unbounded domains

Jie Xu

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 358-396

Abstract: In this paper we shall prove an averaging principle for two-time-scale fractional stochastic parabolic equations on unbounded domains. First, the exponential ergodicity for invariant measures of the fractional stochastic parabolic equation on the unbounded domain Rn is showed. Then an averaging principle for two-time-scale fractional stochastic parabolic equations on unbounded domains is derived. As a byproduct, the rate of strong convergence for the slow component towards the solution of the fractional stochastic parabolic effective equation on the unbounded domain is presented. As far as we know, this is the first result on unbounded domains in this topic.

Keywords: Unbounded domain; Ergodicity; Averaging principle; Strong convergence; Fast–slow; Fractional stochastic parabolic equation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.04.019

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