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arXiv · 2408.00953

Approximation of the invariant measure for stochastic Allen-Cahn equation via an explicit fully discrete scheme

Yibo Wang·Wanrong Cao
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Abstract

In this paper we propose an explicit fully discrete scheme to numerically solve the stochastic Allen-Cahn equation. The spatial discretization is done by a spectral Galerkin method, followed by the temporal discretization by a tamed accelerated exponential Euler scheme. Based on the time-independent boundedness of moments of numerical solutions, we present the weak error analysis in an infinite time interval by using Malliavin calculus. This provides a way to numerically approximate the invariant measure for the stochastic Allen-Cahn equation.

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Yibo Wang, Wanrong Cao. 2024-08-01. Approximation of the invariant measure for stochastic Allen-Cahn equation via an explicit fully discrete scheme. https://doi.org/10.1007/s10543-026-01127-7

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