Existence, Uniqueness and Stability of Solutions for Multidimensional Backward Stochastic Differential Equations with Generators of One-Sided Osgood Type

We establish a general existence and uniqueness result of solution for a multidimensional backward stochastic differential equation (BSDE for short) with generator g satisfying a one-sided Osgood condition as well as a general growth condition in y, and a Lipschitz condition together with a sublinear growth condition in z, which improves some existing results. In particular, we put forward and prove a stability theorem of the solutions for the first time. A new type of solution is also investigated. Some delicate techniques involved in the relationship between convergence in and in probability and dividing appropriately the time interval play crucial roles in our proofs.