一般时间终端一致连续多维BSDE解的稳定性

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.
Abstract：The existence and uniqueness of solutions for general time interval multi-dimensional 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(w, 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.