Forward-backward stochastic differential equations driven by G-Brownian motion under weakly coupling condition

TL;DR

This paper establishes existence, uniqueness, and comparison theorems for coupled forward-backward stochastic differential equations driven by G-Brownian motion, addressing different cases of p and under weakly coupling conditions.

Contribution

It provides the first comprehensive analysis of G-FBSDEs with arbitrary T under weakly coupling, including new results for p in (1,2).

Findings

Proved existence and uniqueness of solutions for G-FBSDEs.

Established comparison theorem under weakly coupling.

Differentiated results for p in (1,2) and p ≥ 2.

Abstract

In this paper, we obtain the existence and uniqueness theorem of $L^{p}$-solution for coupled forward-backward stochastic differential equations driven by G-Brownian motion (G-FBSDEs) with arbitrary $T$ under weakly coupling condition. Specially, the result for $p\in(1,2)$ is completely different from the one for $p\geq2$. Furthermore, by considering the dual linear FBSDE under a suitable reference probability, we establish the comparison theorem for G-FBSDEs under weakly coupling condition.