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

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 $B_{L_t}$ under suitable monotonicity conditions on the coefficients. Here $B$ is a Brownian motion on $\mathbf{R}$ and $L_t:=\inf \{r>0:S_r>t\}$, $t\ge 0,$ is the inverse of a subordinator $S$ with drift $\kappa >0$ that is independent of $B$. Various a priori estimates on the solutions of the FBSDEs are also presented.