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

Xilin Zhou

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arXiv · 2506.10213

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

Xilin Zhou

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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.

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Xilin Zhou. 2025-06-11. Coupling of forward-backward stochastic differential equations on the Wiener space, and application on regularity. https://arxiv.org/abs/2506.10213

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