Multidimensional BSDEs with uniformly continuous generators and general time intervals

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 establish a new existence and uniqueness result for solutions of this kind of backward stochastic differential equations, which extends the results of Hamadene (2003) and Fan, Jiang, Tian (2011) to the general time interval case.