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Orders of convergence in the averaging principle for SPDEs: The case of a stochastically forced slow component

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  • Bréhier, Charles-Edouard

Abstract

This article is devoted to the analysis of semilinear, parabolic, Stochastic Partial Differential Equations, with slow and fast time scales. Asymptotically, an averaging principle holds: the slow component converges to the solution of another semilinear, parabolic, SPDE, where the nonlinearity is averaged with respect to the invariant distribution of the fast process.

Suggested Citation

  • Bréhier, Charles-Edouard, 2020. "Orders of convergence in the averaging principle for SPDEs: The case of a stochastically forced slow component," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3325-3368.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:6:p:3325-3368
    DOI: 10.1016/j.spa.2019.09.015
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    References listed on IDEAS

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    1. Fu, Hongbo & Wan, Li & Liu, Jicheng & Liu, Xianming, 2018. "Weak order in averaging principle for stochastic wave equation with a fast oscillation," Stochastic Processes and their Applications, Elsevier, vol. 128(8), pages 2557-2580.
    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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