Lp solutions of multidimensional BSDEs with weak monotonicity and general growth generators

Abstract

In this paper, we first establish the existence and uniqueness of L p (p > 1) solutions for multidimensional backward stochastic differential equations (BSDEs) under a weak monotonicity condition together with a general growth condition in y for the generator g. Then, we overview several conditions related closely to the weak monotonicity condition and compare them in an effective way. Finally, we put forward and prove a stability theorem and a comparison theorem of L p (p > 1) solutions for this kind of BSDEs.