Existence And Uniqueness Theorem And Stability Theorem For Solutions Of Multidimensional BDSDEs With Continuity Generators

In this thesis, an existence and uniqueness for 2solutions of multidimensional backward doubly stochastic differential equations(BDSDEs for short in the remaining), and a comparison theorem for solution of the class of one-dimensional situation are studied. Further, two kinds of stability theorem for solutions of multidimensional BDSDEs are proposed.In Chapter 1, the backgrounds, the latest status and the content of research, and some useful preliminaries are introduced.In Chapter 2, a class of multidimensional BDSDEs whose generator satisfies the Osgood condition in and generator satisfies non-Lipschitz condition in is studied.First, an existence and uniqueness theorem for 2solutions for this kind of equations is established by the method of a priori estimates and the convolution technique(See Theorem 2.5). This theorem generalizes the corresponding results in both PardouxPeng [1994] and Fan-Jiang-Davison [2013]. Then, a comparison theorem for solution of the class of one-dimensional situation, and a stability theorem of 2solutions for this kind of equations are proposed(See Theorem 2.9, Theorem 2.10).In chapter 3, a stability theorem for 2solutions of multidimensional BDSDEs whose the generators , satisfies the non-Lipschitz condition in is established(See Theorem 3.6).Finally, a summary and prospect of this paper are given in Chapter 4.