Journal of East China Normal University(Natural Science) >

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

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

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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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

Cite this article

DONG Yong-peng , WANG Qian-ru , MA Jiao-jiao . A stability theorem for solutions of general time interval multidimensional BSDEs with uniformly continuous generators[J]. Journal of East China Normal University(Natural Science), 2018 , 2018(1) : 24 -34,49 . DOI: 10.3969/j.issn.1000-5641.2018.01.004

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