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

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  • Xu, Jie

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.

Suggested Citation

  • Xu, Jie, 2022. "An averaging principle for slow–fast fractional stochastic parabolic equations on unbounded domains," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 358-396.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:358-396
    DOI: 10.1016/j.spa.2022.04.019
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    References listed on IDEAS

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    1. Abe, Sumiyoshi & Thurner, Stefan, 2005. "Anomalous diffusion in view of Einstein's 1905 theory of Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 403-407.
    2. Fu, Hongbo & Wan, Li & Liu, Jicheng, 2015. "Strong convergence in averaging principle for stochastic hyperbolic–parabolic equations with two time-scales," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3255-3279.
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