Existence And Uniqueness Of L~1 Solutions To BSDEs With Uniformly Continuous Generators In Z And Continuous Dependence Of L~1 Solutions To A Class Of BSDEs

In this paper, the existence and uniqueness of 1L solutions to the backward stochastic differential equations when the generator is uniformly continuous in z and the problem about the continuous dependence of 1L solutions were mainly discussed by us.In Chapter 1, the background and content of the research was introduced, and we also introduce some preliminaries and lemmas used in the following chapter.The main research results is in the second and third chapter. In chapter 2, the existence and uniqueness of 1L solutions when the generator is Osgood continuous in y, uniformly continuous and a linear growth condition in z,was mainly discussed by us, we also obtain a comparison theorem and prove the existence and uniqueness of 1L solutions under this condition. It generalizes the results of Tian-Jiang-Shi[2012]. In chapter 3,a preliminary study about the continuous dependence of integrable solutions was conducted by us, and we prove the continuous dependence theorem of 1L solutions when the generator is just Lipschitz continuous in y. And we extend to the more general case that the generator is just Osgood condition in y. In Chapter 4, we look to the prospects for the 1L solutions to the backward stochastic differential equations and put forward two questions.