Coupling of forward-backward stochastic differential equations on the Wiener space, and application on regularity

Xilin Zhou

Coupling of forward-backward stochastic differential equations on the Wiener space, and application on regularity

Probability 2025-06-13 v1

Authors: Xilin Zhou

Abstract

S. Geiss and J. Ylinen proposed the coupling method \cite{Geiss:Ylinen:21} to investigate the regularity for the solution to the backward stochastic differential equations with random coefficients. In this paper, we explore this method in setting for the forward-backward stochastic differential equation with random and Lipschitz coefficients, We obtain the regularity in time, and the Malliavin Sobolev ${\mathbb D}_{1,2}$ differentiability for the solution.

Keywords

forward-backward stochastic differential equations coupling method Wiener space regularity Malliavin Sobolev differentiability random Lipschitz coefficients

Cite

@article{arxiv.2506.10213,
  title  = {Coupling of forward-backward stochastic differential equations on the Wiener space, and application on regularity},
  author = {Xilin Zhou},
  journal= {arXiv preprint arXiv:2506.10213},
  year   = {2025}
}

Related papers

View all related →