Modern Stochastics: Theory and Applications

In this paper, we study multidimensional generalized BSDEs that have a monotone generator in a general filtration supporting a Brownian motion and an independent Poisson random measure. First, we prove the existence and uniqueness of ${\mathbb{L}}^{p}(p\ge 2)$-solutions in the case of a fixed terminal time under suitable p-integrability conditions on the data. Then, we extend these results to the case of a random terminal time. Furthermore, we provide a comparison result in dimension 1.

Our aim in this paper is to establish some strong stability properties of a solution of a stochastic differential equation driven by a fractional Brownian motion for which the pathwise uniqueness holds. The results are obtained using Skorokhod’s selection theorem.