Explicit domain preserving numerical schemes for a class of stochastic differential equations

Charles-Edouard Bréhier; David Cohen

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arXiv · 2608.25685

Explicit domain preserving numerical schemes for a class of stochastic differential equations

Charles-Edouard Bréhier·David Cohen

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Abstract

We construct and analyze numerical schemes for systems of stochastic differential equations, which preserve almost surely a given hypercube of arbitrary dimension. We propose a new general class of explicit schemes, such that for any choice of the time-step size the numerical solution takes values in the hypercube. We prove strong and weak convergence results for this general class of domain preserving numerical schemes, with strong order $1/2$ and weak order $1$ in general. We also construct a variant of the scheme which achieves strong order $1$ when the stochastic differential equation is driven by a one-dimensional Brownian motion. The convergence results are illustrated with numerical experiments.

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Charles-Edouard Bréhier, David Cohen. 2026-08-26. Explicit domain preserving numerical schemes for a class of stochastic differential equations. https://arxiv.org/abs/2608.25685

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