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

2025/06/11 by Zhou, Xilin
#46E35 #60H07 #60H10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.10213

Abstract

S. Geiss and J. Ylinen proposed the coupling method \citeGeiss: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.

Citations

• Time discretization of Quadratic Forward-Backward SDEs with singular drifts
• Differentiability of quadratic forward-backward SDEs with rough drift
• Path regularity of coupled McKean-Vlasov FBSDEs
• Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs
• Existence, Uniqueness and Regularity of Decoupling Fields to Multidimensional Fully Coupled FBSDEs

Related

• Regularity of stochastic differential equations on the Wiener space by coupling
• Strong solutions of forward-backward stochastic differential equations with measurable coefficients
• Zhang L²-Regularity for the solutions of Backward Doubly Stochastic Differential Equations under globally Lipschitz continuous assumptions
• Path regularity of coupled McKean-Vlasov FBSDEs
• Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs