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arXiv · 2311.15151

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

Shuaiqi Zhang·Zhen-Qing Chen
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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 $\bf R$ and $L_t:= \inf\{r>0: S_r>t\}$, $t\geq 0,$ 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.

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Shuaiqi Zhang, Zhen-Qing Chen. 2023-11-26. Fully coupled forward-backward stochastic differential equations driven by sub-diffusions. https://arxiv.org/abs/2311.15151

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