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
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
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