Existence, Uniqueness And Comparison Theorems For L~p (p>1) Solutions Of One-dimensional BSDEs Under The Weak Monotonicity Condition

This paper mainly studies the existence, uniqueness and comparison theorem for Lp (p>1) solutions of one-dimensional backward stochastic differential equations (BSDEs for short in the remaining), whose generator g satisfies a weak monotonicity condition in y, and a uniform continuity condition and a linear growth condition in z respectively. These results generalize some existing results.In Chapter 1, we briefly introduce the research background and status, research contents and some preliminaries.In Chapter 2, we prove the existence and uniqueness for Lp solutions of one-dimensional BSDEs (see Theorem 2.1), where the generator g is (p^2)-order weak monotonic with a general growth in y and is uniformly continuous in z. This generalizes some corresponding results in Jia [2008a], Chen [2010], Ma-Fan-Song [2013] and Fan [2015] in the one-dimensional case setting.In Chapter 3, we establish a comparison theorem (see Theorem 3.1) for Lp solu-tions of one-dimensional BSDEs, whose generator g satisfies a p-order weak mono-tonicity condition in y and a uniform continuity condition in z, which generalizes the result in Fan [2015].In Chapter 4, by using the convolution technique and localization procedure, we put forward and prove an existence result for a minimal (maximal) Lp (p> 1) solution of one-dimensional BSDEs (see Theorem 4.1), where the generator g satisfies a (p^2)-order weak monotonicity condition with a general growth condition in y, and a linear growth condition in z.Chapter 5 summarizes some conclusions and innovations, and gives some ideas for future research.