L^p–estimates of Solutions of Backward Doubly Stochastic Differential Equations

Abstract

This paper deals with a large class of nonhomogeneous backward doubly stochastic differential equations which have a more general form of the forward Itˆo integrals. Terms under which the solutions of these equations are bounded in the L p -sense, p ≥ 2, under both the Lipschitz and non-Lipschitz conditions, are given, i.e. L p – stability for this general type of backward doubly stochastic differential equations is
established.