Fully coupled forward-backward stochastic differential equations driven by sub-diffusions

2023/11/26 by Zhang, Shuaiqi, Chen, Zhen-Qing
#60H10 #60K50 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2311.15151

Abstract

In this paper, we establish the existence and uniqueness of fully coupled forward-backward stochastic differential equations (FBSDEs in short) driven by anomalous sub-diffusions B_Lt under suitable monotonicity conditions on the coefficients. Here B is a Brownian motion on \bf R and L_t:= inf\r>0: S_r>t\, t≥ 0, is the inverse of a subordinator S with drift κ>0 that is independent of B. Various a priori estimates on the solutions of the FBSDEs are also presented.

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