Lp (p ≥ 1) solutions of multidimensional BSDEs with monotone generators in general time intervals

In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equation in L-p (p >= 1). We first study the existence and uniqueness for L-p (p > 1) solutions by the method of convolution and weak convergence when the generator is monotonic in y and Lipschitz continuous in z both non-uniformly with respect to t. Then we obtain the existence and uniqueness for L-1 solutions with an additional assumption that the generator has a sublinear growth in z non-uniformly with respect to t.