Numerical Computation for Backward Doubly SDEs with random terminal time

Anis Matoussi (1) , Wissal Sabbagh (2)

1 LMM - Laboratoire Manceau de Mathématiques
2 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

In this article, we are interested in solving numerically backward doubly stochastic differential equations (BDSDEs) with random terminal time tau. The main motivations are giving a probabilistic representation of the Sobolev's solution of Dirichlet problem for semilinear SPDEs and providing the numerical scheme for such SPDEs. Thus, we study the strong approximation of this class of BDSDEs when tau is the first exit time of a forward SDE from a cylindrical domain. Euler schemes and bounds for the discrete-time approximation error are provided.

Mots clés: and phrases: Backward Doubly Stochastic Differential Equation; Monte carlo; method; Euler scheme; Exit time; Stochastic flow; SPDEs; Dirichlet condition

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Anis Matoussi, Wissal Sabbagh. Numerical Computation for Backward Doubly SDEs with random terminal time. 2018. ⟨hal-01740713⟩