Existence, Uniqueness And Stability For Solutions Of Two Kinds Of Multidimensional BSDEs Under The Uniform Continuity Condition

In this paper, the existence, uniqueness and stability for solutions of two kinds of multidimensional backward stochastic differential equations(BSDEs for short) with uniform continuity generators in z is mainly studied, which generalizes some existing results.In Chapter 1, the background, the latest status, the content of research and some useful preliminaries are briefly introduced.In Chapter 2, an existence and uniqueness result of Lp(p > 1) solutions for multidimensional BSDEs(see Theorem 2.5) is put forward and proved, where the generator g satisfies a certain one-sided Osgood condition with a general growth in y as well as a uniform continuity condition in z, and the i-th componentig of g depends only on the i-th rowiz of matrix z besides(ω, t, y). Furthermore, the stability theorem of Lp(p > 1) solutions for the this kinds of BSDEs(see Theorem 2.11) is also put forward and proved. This generalizes some corresponding results obtained in El Karoui-PengQuenez [1997], Pardoux [1999], Fan-Jiang [2013] and Fan [2014].In Chapter 3, a stability theorem of L2 solutions for finite and infinite time interval multidimensional BSDEs(see Theorem 3.5) is established and proved, where the generator g satisfies a Osgood condition in y and a uniformly continuous condition in z both non-uniformly with respect to t. This conclusion extends the stability theorem of solutions to the infinite time interval case.Finally, a summary and prospect of this paper is given in Chapter 4.