Numerical scheme for backward doubly stochastic differential equations

Auguste Aman (1)

1 LMAI - Laboratoire de Mathématiques Appliquées et Informatique

We study a discrete-time approximation for solutions of systems of decoupled forward-backward doubly stochastic differential equations (FBDSDEs). Assuming that the coefficients are Lipschitz-continuous, we prove the convergence of the scheme when the step of time discretization, $|\pi|$ goes to zero. The rate of convergence is exactly equal to $|\pi|^{1/2}$. The proof is based on a generalization of a remarkable result on the $^{2}$-regularity of the solution of the backward equation derived by J. Zhang

Mots clés: Backward doubly SDEs; Discrete-time approximation

Domaines: Probabilités [math.PR]

Auguste Aman. Numerical scheme for backward doubly stochastic differential equations. 2009. ⟨hal-00403667⟩