华东师范大学学报（自然科学版） >

2018 , Vol. 2018 >Issue 1: 24 - 34,49

DOI: https://doi.org/10.3969/j.issn.1000-5641.2018.01.004

数学

一般时间终端一致连续多维BSDE解的稳定性

  • 董勇鹏 ,
  • 王茜茹 ,
  • 马娇娇
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  • 中国矿业大学 数学学院, 江苏 徐州 221116
董勇鹏,男,硕士研究生,研究方向为倒向随机微分方程.E-mail:yong_p_dong@163.com.

收稿日期: 2017-01-09

  网络出版日期: 2018-01-11

基金资助

国家自然科学基金（11371362）

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

  • DONG Yong-peng ,
  • WANG Qian-ru ,
  • MA Jiao-jiao
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  • School of Mathematics, China University of Mining and Technology, Xuzhou Jiangsu 221116, China

Received date: 2017-01-09

  Online published: 2018-01-11

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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.

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

本文引用格式

董勇鹏 , 王茜茹 , 马娇娇 . 一般时间终端一致连续多维BSDE解的稳定性[J]. 华东师范大学学报（自然科学版）, 2018 , 2018(1) : 24 -34,49 . DOI: 10.3969/j.issn.1000-5641.2018.01.004

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.

Key words： multidimensional backward stochastic differential equation; stability theorem; uniformly continuous condition; general time interval

参考文献

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