一般时间终端一致连续多维BSDE解的稳定性  

A stability theorem for solutions of general time interval multidimensional BSDEs with uniformly continuous generators

作　　者：董勇鹏 王茜茹 马娇娇 DONG Yong-peng;WANG Qian-ru;MA Jiao-jiao(School of Mathematics, China University of Mining and Technology, Xuzhou Jiangsu 221116,China)

机构地区：[1]中国矿业大学数学学院,江苏徐州221116

出　　处：《华东师范大学学报（自然科学版）》2018年第1期24-34,49,共12页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11371362)

摘　　要：在生成元g关于y满足对t不一致的Osgood条件,关于z满足对t不一致的一致连续条件且g的第i个分量仅仅依赖于(w,t,y)及矩阵z的第i行的条件下,范胜君等在2015年证明了一般时间终端多维倒向随机微分方程(简称BSDE)解的存在性和唯一性.在此基础上,本文利用一致连续函数可用Lipschitz函数一致逼近的性质、迭代技术、Girsanov变换及Bihari不等式等工具,首次建立了上述条件下一般时间终端多维BSDE解的一个稳定性定理.The existence and uniqueness of solutions for general time interval multidimensional backward stochastic differential equations(BSDEs)was proved in Fan et al.(2015)under assumptions that the generator g satisfies the Osgood condition in y and the uniformly continuous condition in z both non-uniformly with respect to t,and the i-th component gi of g depends only on(u,t,y)and the i-th row of the matrix z.In this paper,by virtue of a uniform approximation of uniformly continuous functions by a sequence of Lipschitz functions,the theorem of Girsanov,and the Bihari inequality,we establish,for the first time,a stability theorem for the solutions of the general time interval multidimensional BSDEs with uniformly continuous generators.

关 键 词：多维倒向随机微分方程 稳定性定理 一致连续 一般时间终端 

分 类 号：O157.5[理学—数学]