𝕃2-solutions of multidimensional generalized BSDEs with weak monotonicity and general growth generators in a general filtration

Abstract

Abstract In this paper, we study multidimensional generalized backward stochastic differential equations (GBSDEs), in a general filtration supporting a Brownian motion and an independent Poisson random measure, whose generators are weakly monotone and satisfy a general growth condition with respect to the state variable y. We show that such GBSDEs admit a unique 𝕃 2 {\mathbb{L}^{2}} -solution. The main tools and techniques used in the proofs are the a-priori-estimation, the convolution approach, the iteration, the truncation, and the Bihari inequality.