$L^p$ $(p\geq 1)$ solutions of multidimensional BSDEs with time-varying quasi-H\"older continuity generators in general time intervals
Commun. Korean Math. Soc.
Published online January 30, 2020
Xiao Lishun and Fan Shengjun
Xuzhou Medical University, China University of Mining and Technology
Abstract : The objective of this paper is solving $L^p$ $(p\geq 1)$ solutions of multidimensional backward stochastic differential equations with general time intervals, where the generator $g$ satisfies a time-varying Osgood condition in $y$, a time-varying quasi-H\"older continuity condition in $z$, and its $i$th component depends on the $i$th row of $z$. Our result strengthens some existing works even though for the case of finite time intervals.
Keywords : Backward stochastic differential equation; $L^p$ $(p\geq 1)$ solution; General time interval; Osgood condition; quasi-H\"older continuity
MSC numbers : 60H10
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