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

2022/11/28 by Li, Xiaojuan
#60H10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2211.15041

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∈(1,2) is completely different from the one for p≥2. Furthermore, by considering the dual linear FBSDE under a suitable reference probability, we establish the comparison theorem for G-FBSDEs under weakly coupling condition.

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