Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme

TL;DR

This paper establishes well-posedness for stochastic sweeping processes and demonstrates convergence of a related Euler scheme, integrating deterministic theory with stochastic reflection methods.

Contribution

It introduces new well-posedness results for stochastic sweeping processes and proves convergence of a numerical Euler scheme for these inclusions.

Findings

Well-posedness results for stochastic sweeping processes.

Convergence proof for the Euler discretization scheme.

Integration of deterministic sweeping theory with stochastic reflection techniques.

Abstract

Here we present well-posedness results for first order stochastic differential inclusions, more precisely for sweeping process with a stochastic perturbation. These results are provided in combining both deterministic sweeping process theory and methods concerning the reflection of a Brownian motion. In addition, we prove convergence results for a Euler scheme, discretizing theses stochastic differential inclusions.