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

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 (recently developed in Edmond and Thibault (2005, 2006) [18,19]) and methods concerning the reflection of a Brownian motion (Lions and Sznitman, 1984 [23], and Saisho, 1987 [31]). In addition, we prove convergence results for an Euler scheme, discretizing these stochastic differential inclusions.