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

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