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

DONG Yong-peng; WANG Qian-ru; MA Jiao-jiao

doi:10.3969/j.issn.1000-5641.2018.01.004

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Jan. 2018

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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 Sciences), 2018, (1): 24-34, 49. doi: 10.3969/j.issn.1000-5641.2018.01.004

Citation:

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 Sciences), 2018, (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

doi: 10.3969/j.issn.1000-5641.2018.01.004

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

Received Date: 2017-01-09
Publish Date: 2018-01-25

Abstract

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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References(10)

References

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