Lp - 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 Itô 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.

Some analytic approximations for backward stochastic differential equations

“…Ðordević [5] proved the closeness result for the general type of perturbations for reflected BSDEs. For backward doubly stochastic differential equations Ðordević et al [3,4,11] proved existence result for nonhomogeneous class od equations, L p stability and obtained a generalization of the well-known Feynman Kac formula for those equations (all those problems are proved under several different conditions).…”