L~p Solutions Of Anticipated BSDEs With Non-lipschitz Conditions

In this paper,we study the existence and uniqueness result of solutions for anticipated backward stochastic differential equations and anticipated backward doubly stochastic differential equations.In chapter 1,we establish the existence and uniqueness result of L~p(1<p≤2)solutions for anticipated backward stochastic differential equations,in which the generator satisfies non-Lipschitz conditions.Firstly,by constructing contraction mapping and using fixed point theorem,we obtain the existence and uniqueness of L~psolutions of anticipated backward stochastic differential equations satisfying the Lipschitz condition.Secondly,we establish the existence and uniqueness result of L~psolutions to the anticipated backward stochastic differential equations satisfying the Lipschitz condition by constructing the sequence of Picard-type iteration.In chapter 2,we study the existence and uniqueness result of solutions for anticipated backward doubly stochastic differential equations whose generators not only depend on the anticipated terms of the solution(Y_·,Z_·)but also satisfy one kind of non-Lipschitz assumption.Two comparison theorems for the solutions of these equations are obtained after finding a new comparison theorem for backward doubly stochastic differential equa-tions with non-Lipschitz coefficients.