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

doi:10.3969/j.issn.1000-5641.2018.01.004

一般时间终端一致连续多维BSDE解的稳定性

doi: 10.3969/j.issn.1000-5641.2018.01.004

中国矿业大学数学学院, 江苏徐州 221116

基金项目:

国家自然科学基金 11371362

详细信息

作者简介:
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

中图分类号: O157.5
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出版历程
- 收稿日期: 2017-01-09
- 刊出日期: 2018-01-25

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

School of Mathematics, China University of Mining and Technology, Xuzhou Jiangsu 221116, China

摘要

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.
- 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
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 g_i 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.
- multidimensional backward stochastic differential equation /
- stability theorem /
- uniformly continuous condition /
- general time interval

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参考文献(10)

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