Existence And Uniqueness Of L~p(p≥1) Solutions For General Time Interval BSDEs With Generators Satisfying Some Stochasticity And Monotonicity Conditions

This paper mainly studies Lp(p≥1) solutions of finite and infinite time interval backward stochastic differential equations (BSDEs for short) with generators in satisfy-ing some stochasticity conditions non-uniform in both ω and t, which generalizes some existing results.In Chapter 1, the research backgrounds, research contents and significance and some useful preliminaries are briefly introduced.In Chapter 2, an existence and uniqueness result for Lp(p> 1) solutions of finite and infinite time interval multidimensional BSDEs (see Theorem 2.3) is put forward and proved, where the generator is monotonic and has a general growth in y, and is Lips-chitz continuous in z, both non-uniformly with respect to both ω and t. This conclusion extends the corresponding results obtained in Briand-Delyon-Hu-Pardoux-Stoica [2003] and Xiao-Fan-Xu [2015].In Chapter 3, the existence and uniqueness result for L1 solutions of the above BSDEs with an additional assumption that the generator has a sublinear growth in z non-uniformly with respect to both ω and t (see Theorem 3.1) is established, which gen-eralizes the corresponding result of L1 solutions in Briand-Delyon-Hu-Pardoux-Stoica [2003] and Xiao-Fan-Xu [2015].In Chapter 4, we prove the existence and uniqueness for Lp(p> 1) solutions of finite and infinite time interval one-dimensional BSDEs (see Theorem 4.2), where the generator is monotonic and has a general growth in y, and is uniformly continuous in z, both non-uniformly with respect to both ω and t. This conclusion generalizes the corresponding result in Ma-Fan-Song [2013]. Furthermore, the existence of a minimal Lp(p> 1) solution of finite and infinite time interval one-dimensional BSDEs (see The-orem 4.3) is established under the condition that the generator has a linear growth in z non-uniformly with respect to both ω and t, which improves the corresponding result in Briand-Lepeltier-San Martin [2007].In Chapter 5, summarizes and prospects of this paper are given.