## Brazilian Journal of Probability and Statistics

### On the stability theorem of $L^{p}$ solutions for multidimensional BSDEs with uniform continuity generators in $z$

#### 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.

#### Article information

Source
Braz. J. Probab. Stat., Volume 30, Number 2 (2016), 321-344.

Dates
Accepted: January 2015
First available in Project Euclid: 31 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1459429715

Digital Object Identifier
doi:10.1214/15-BJPS282

Mathematical Reviews number (MathSciNet)
MR3481106

Zentralblatt MATH identifier
1341.60056

#### Citation

Ma, Jiaojiao; Fan, Shengjun; Fang, Rui. On the stability theorem of $L^{p}$ solutions for multidimensional BSDEs with uniform continuity generators in $z$. Braz. J. Probab. Stat. 30 (2016), no. 2, 321--344. doi:10.1214/15-BJPS282. https://projecteuclid.org/euclid.bjps/1459429715

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