Existence And Stability Theorem Of L~p(p>1) Solutions For One-dimensional BSFEs Under The Weak Monotonicity Conditions

In this paper,we mainly study the existence theorem,comparison theorem and stabil-ity result of L^psolutions for one-dimensional backward stochastic differential equations（BSDEs for short）with weak monotonicity condition,which extends,to a certain extent,some of corresponding results obtained in exiting references.Chapter 1 briefly introduces the background of the study,the research status,the research content,and some preparatory knowledge.In Chapter 2,we start with establishing the existence and uniqueness for L^psolutions of one-dimensional BSDEs（see Theorem 2.1）,where the generator is（p∧2）-order weak monotonic with a general growth in y and Lipschitz continuous in z.Furthermore,we prove the existence of a minimal（maximal）L^p（p>1）solution to a one-dimensional BSDEs（see Theorem 2.2）by virtue of the convolution technique in Lepeltier-San Martín[1997]and the localization method first developed by Briand-Lepeltier-San Martín[2007],whose the generator g can be decomposited as g₁+g₂.g₁satisfies a p-order weak monotonicity condition and a certain general growth in y and a kind of linear growth condition in z,g₂is of linear growth in（y,z）,left-continuous and lower semi-continuous（right-continuous and upper semi-continuous）in y,and continuous in z.Note that the generator g may be discontinuous in y.Then in view of It?’s formula and Tanaka’s formula,the comparison theorem and Levi type theorem of a minimal（maximal）L^p（p>1）solution to one-dimensional BSDEs have been proposed.These generalize some previous results in Briand-Lepeltier-San Martín[2007],Fan-Jiang[2012b],Ma-Fan-Song[2013]and Fan[2015]in one-dimensional case.In Chapter 3,we propose and prove a stability theorem of L^psolutions for one-dimensional BSDEs,where the generator g satisfies a p-order one-sided Mao’s condition in y and a uniform continuity condition in z.This generalizes the corresponding results in Jia[2010].Chapter 4 makes a brief summary and prospect for the results obtained and the techniques used in this article.