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

Frederic Bernicot (1) , Juliette Venel (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

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.

Mots clés: Sweeping process; differential inclusions; stochastic differential equations; Euler scheme

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]; Analyse numérique [math.NA]

Frederic Bernicot, Juliette Venel. Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme. Journal of Differential Equations, 2011, 251 (4-5), pp.1195-1224. ⟨10.1016/j.jde.2011.03.010⟩. ⟨hal-00448064⟩