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arXiv · 2609.29950

Domain preserving splitting schemes for a class of SPDEs driven by a standard Brownian motion

Charles-Edouard Bréhier·David Cohen·Gijs Custers
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Abstract

We consider a class of SPDEs driven by a standard real-valued Brownian motion, with drift and diffusion coefficients such that there exists a unique mild solution taking values in the interval $[-1,1]$ almost surely. To preserve this qualitative property of the exact solution, we propose a domain preserving Lie--Trotter splitting scheme: for any choice of the time-step size, the numerical solution takes values in the interval $[-1,1]$ almost surely. Furthermore, we prove mean-square convergence with rate $1/2-$ for the domain preserving Lie--Trotter scheme. These theoretical results are illustrated with numerical experiments.

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Charles-Edouard Bréhier, David Cohen, Gijs Custers. 2026-09-24. Domain preserving splitting schemes for a class of SPDEs driven by a standard Brownian motion. https://arxiv.org/abs/2609.29950

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