$\mathbb{L}^p$-solution of generalized BSDEs in a general filtration with stochastic monotone coefficients

Badr Elmansouri; Mohamed El Otmani

$\mathbb{L}^p$-solution of generalized BSDEs in a general filtration with stochastic monotone coefficients

Probability 2025-01-28 v1

Authors: Badr Elmansouri , Mohamed El Otmani

Abstract

We study multidimensional generalized backward stochastic differential equations (GBSDEs) within a general filtration that supports a Brownian motion under weak assumptions on the associated data. We establish the existence and uniqueness of solutions in $\mathbb{L}^p$ for $p \in (1,2]$ . Our results apply to generators that are stochastic monotone in the $y$ -variable, stochastic Lipschitz in the $z$ -variable, and satisfy a general stochastic linear growth condition.

Keywords

backward stochastic differential equations general filtration stochastic monotonicity $\mathbb{L}^p$ solution Lipschitz condition

Cite

@article{arxiv.2501.15600,
  title  = {$\mathbb{L}^p$-solution of generalized BSDEs in a general filtration with stochastic monotone coefficients},
  author = {Badr Elmansouri and Mohamed El Otmani},
  journal= {arXiv preprint arXiv:2501.15600},
  year   = {2025}
}

Related papers

View all related →