Multidimensional BSDEs with uniformly continuous generators and general time intervals
Bull. Korean Math. Soc. 2015 Vol. 52, No. 2, 483-504
Published online March 31, 2015
Shengjun Fan, Yanbin Wang, and Lishun Xiao
Fudan University, China University of Mining and Technology, China University of Mining and Technology
Abstract : 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
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