Optimal convergence rates in the averaging principle for slow-fast SPDEs driven by multiplicative noise

Yi Ge; Xiaobin Sun; Yingchao Xie

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arXiv · 2101.09076

Optimal convergence rates in the averaging principle for slow-fast SPDEs driven by multiplicative noise

Yi Ge·Xiaobin Sun·Yingchao Xie

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Abstract

In this paper, we study a class of slow-fast stochastic partial differential equations with multiplicative Wiener noise. Under some appropriate conditions, we prove the slow component converges to the solution of the corresponding averaged equation with optimal orders 1/2 and 1 in the strong and weak sense respectively. The main technique is based on the Poisson equation.

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Yi Ge, Xiaobin Sun, Yingchao Xie. 2021-01-22. Optimal convergence rates in the averaging principle for slow-fast SPDEs driven by multiplicative noise. https://arxiv.org/abs/2101.09076

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