Backward Doubly Stochastic Differential Equations with Weak Regularity Coefficients: Existence in Lp

Abstract

This work is devoted to the study of multidimensional backward doubly stochastic differential equations under weak regularity assumptions on the coefficients. In particular, we introduce a new class of non-Lipschitz conditions and show that the associated BDSDEs admit a unique solution in Lp for any p > 1. Several classical results are recovered as particular cases of our analysis.