Bull. Korean Math. Soc. 2015; 52(2): 483-504
Printed March 31, 2015
https://doi.org/10.4134/BKMS.2015.52.2.483
Copyright © The Korean Mathematical Society.
Shengjun Fan, Yanbin Wang, and Lishun Xiao
Fudan University, China University of Mining and Technology, China University of Mining and Technology
This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in $(y,z)$ non-uniformly with respect to $t$. By establishing some results on deterministic backward differential equations with general time intervals, and by virtue of Girsanov's theorem and convolution technique, we prove a new existence and uniqueness result for solutions of this kind of backward stochastic differential equations, which extends the results of \cite{Hamadene2003Bernoulli} and \cite{FanJiangDavison2010CRASSI} to the general time interval case.
Keywords: backward stochastic differential equation, general time interval, existence and uniqueness, uniformly continuous generator
MSC numbers: 60H10
2018; 55(6): 1639-1657
2013; 50(4): 1079-1086
2005; 42(4): 829-836
2006; 43(2): 319-331
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd