Year: 2025
Author: Zhihui Liu
Communications in Mathematical Research , Vol. 41 (2025), Iss. 1 : pp. 30–44
Abstract
We establish the unique ergodicity of a fully discrete scheme for monotone SPDEs with polynomial growth drift and bounded diffusion coefficients driven by multiplicative white noise. The main ingredient of our method depends on the satisfaction of a Lyapunov condition followed by a uniform moments’ estimate, combined with the regularity property for the full discretization. We transform the original stochastic equation into an equivalent random equation where the discrete stochastic convolutions are uniformly controlled to derive the desired uniform moments’ estimate. Applying the main result to the stochastic Allen-Cahn equation driven by multiplicative white noise indicates that this full discretization is uniquely ergodic for any interface thickness. Numerical experiments validate our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2024-0042
Communications in Mathematical Research , Vol. 41 (2025), Iss. 1 : pp. 30–44
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Numerical invariant measure numerical ergodicity stochastic Allen-Cahn equation.
Author Details
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Numerical Unique Ergodicity of Monotone SDEs Driven by Nondegenerate Multiplicative Noise
Liu, Zhihui
Liu, Zhizhou
Journal of Scientific Computing, Vol. 103 (2025), Iss. 3
https://doi.org/10.1007/s10915-025-02902-4 [Citations: 0]