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

Published 22 Jan 2021 in math.PR | (2101.09076v2)

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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