Journal of East China Normal University(Natural Sc ›› 2018, Vol. 2018 ›› Issue (1): 24-34,49.doi: 10.3969/j.issn.1000-5641.2018.01.004

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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   

  1. School of Mathematics, China University of Mining and Technology, Xuzhou Jiangsu 221116, China
  • Received:2017-01-09 Online:2018-01-25 Published:2018-01-11

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

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