Lp Solutions Of Backward Doubly Stochastic Differential Equations With Non-Lipschitz Conditions

This thesis mainly studies two parts.The first part interested in solving a class of backward doubly stochastic differential equations(BDSDEs in short)whose generator f with respect to y satisfying the non-Lipschitz continuous condition and with respect to z satisfying the Lipschitz continuous condition,generator g with respect to y and z satisfying the uniform Lipschitz continuous condition.We establish the existence and uniqueness theorem of solution of BDSDEs in L~p,p∈(1,2].The second part we explore a new class of stochastic differential equations called anticipated generalized backward doubly stochastic differential equations(AGBDSDEs in short)which not only involves two symmetric integrals related to two independent Brown motions and an integral driven by continuous increasing process but also includes generators depending on the anticipated terms of the solution(Y,Z).Firstly,we prove existence and uniqueness theorem for AGBDSDEs.Further,two comparison theorems for AGBDSDEs are obtained after finding a new comparison theorem for generalized backward doubly stochastic differential equations(GBDSDEs in short).