Stability Theorems For Solutions Of Several Kinds Of One-dimensional BSDES Under The Uniform Continuity Condition And Its Applications

In this paper, some stability theorems for solutions of several kinds of onedimensional backward stochastic differential equations(BSDEs for short) with uniformly continuous generators are mainly studied and some existing results are generalized.In Chapter 1, the background on BSDEs, research contents and some preliminaries for the following chapters are briefly introduced.In Chapter 2, a stability theorem for solutions of one-dimensional BSDEs is put forward and proved by establishing an inequality between conditional mathematic expectations of random variables under two different but equivalent probability measures,where generator g is monotonic in y and uniformly continuous in z. This result generalizes the corresponding results in El Karoui-Peng-Quenez [1997], Pardoux [1999]and Jia [2010] for the one-dimensional case.In Chapter 3, a general stability theorem for solutions of one-dimensional BSDEs is established, where generator g satisfies a uniformly continuous condition in z. As an application of this stability theorem, a general existence and uniqueness for solutions of one-dimensional BSDEs is proved, where generator g satisfies a one-sided Constantin condition in y and a uniform continuity condition in z. This generalizes some corresponding results in Constantin [2001], Pardoux [1999], Fan-Jiang [2010b] and Jia[2010] for the one-dimensional case.In Chapter 4, a monotonic limit theorem for solutions of one-dimensional BSDEs is established and its generator g satisfies a one-sided Osgood condition in y and a uniformly continuous condition in z. Some corresponding results in Fan-Wu-Zhu[2007], Ma-Fan-Song [2014] are improved.Finally, a summary and prospect of this paper are given in Chapter 5.