Communications of the
Korean Mathematical Society CKMS

The objective of this paper is solving multidimensional backward stochastic differential equations with general time intervals, in $L^p$ $(p\geq 1)$ sense, 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 for the case of finite time intervals.

Keywords: Backward stochastic differential equation, $L^p$ $(p\geq 1)$ solution, general time interval, quasi-H\"older continuity

MSC numbers: 60H10

Supported by: Xiao Lishun is supported by the Research Initiation Foundation of Xuzhou Medical
University (No. D2018002) and the National Natural Science Foundation of China (Nos.
11601509 and 31801957), and Fan Shengjun is supported by the National Fund for Study
Abroad (No. 201806425013).