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May 2016 On the stability theorem of $L^{p}$ solutions for multidimensional BSDEs with uniform continuity generators in $z$
Jiaojiao Ma, Shengjun Fan, Rui Fang
Braz. J. Probab. Stat. 30(2): 321-344 (May 2016). DOI: 10.1214/15-BJPS282

Abstract

In this paper, we first establish an existence and uniqueness result of $L^{p}$ ($p>1$) solutions for multidimensional backward stochastic differential equations (BSDEs) whose generator $g$ satisfies a certain one-sided Osgood condition with a general growth in $y$ as well as a uniform continuity condition in $z$, and the $i$th component ${}^{i}g$ of $g$ depends only on the $i$th row ${}^{i}z$ of matrix $z$ besides $(\omega,t,y)$. Then we put forward and prove a stability theorem for $L^{p}$ solutions of this kind of multidimensional BSDEs. This generalizes some known results.

Citation

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Jiaojiao Ma. Shengjun Fan. Rui Fang. "On the stability theorem of $L^{p}$ solutions for multidimensional BSDEs with uniform continuity generators in $z$." Braz. J. Probab. Stat. 30 (2) 321 - 344, May 2016. https://doi.org/10.1214/15-BJPS282

Information

Received: 1 December 2014; Accepted: 1 January 2015; Published: May 2016
First available in Project Euclid: 31 March 2016

zbMATH: 1341.60056
MathSciNet: MR3481106
Digital Object Identifier: 10.1214/15-BJPS282

Rights: Copyright © 2016 Brazilian Statistical Association

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Vol.30 • No. 2 • May 2016
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