Existence And Uniqueness For Solutions Of Two Kinds Of Multidimensional BSDEs

In this paper, we mainly study the existence and uniqueness for solutions of twokinds of backward stochastic differential equations (BSDEs for short), which general-izes some existing results.Chapter1of this paper briefly introduces the background on BSDEs, researchcontents and some preliminaries for the following chapters.Chapter2studies the existence and uniqueness for L2solutions of finite time in-terval multidimensional BSDEs (See Theorem2.2) by the method of the truncation,Picard iteration, Bihari’s inequality and apriori estimates, where the generators satisfythe weakly monotonicity condition and the generalized general growth condition in y,and is Lipschitz continuous in z. This result generalizes the corresponding results inMao [1995], Pardoux [1999] and Fan-Jiang [2013].Chapter3proves the existence and uniqueness of Lp(p>1) solutions for finitetime interval multidimensional BSDEs (See Theorem3.2) via the truncation, Picarditeration, Bihari’s inequality and apriori estimates, where the generators satisfy the p-order one-sided Mao’s condition and generalized general growth condition in y, andis Lipschitz continuous in z. At last, it also introduce some remarks, corollaries andexamples to show that Theorem3.2generalizes the corresponding results in both Briandet al.[2003] and Fan-Jiang [2014].Finally, Chapter4gives a summary and prospect of this paper.