Reflected Backward Doubly Stochastic Differential Equations and Application

Auguste Aman (1) , Modeste Nzi (1)

1 LMAI - Laboratoire de Mathématique Appliquées et informatiques

This paper is devoted to study the class of reflected backward doubly stochastic differ- ential equation (RBDSDE, for short). We first prove existence and uniqueness result under Lipschitz condition on the coefficient (drift) via the penalization method. As application we derive the obstacle problem of stochastic PDE.

Mots clés: Backward doubly SDEs; Stochastic PDE; Obstacle problem.; Obstacle problem

Domaines: Probabilités [math.PR]

Auguste Aman, Modeste Nzi. Reflected Backward Doubly Stochastic Differential Equations and Application. 2007. ⟨hal-00199360⟩