Bulletin of the
Korean Mathematical Society BKMS

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