Asymptotic Properties of Coupled Forward-Backward Stochastic Differential Equations

TL;DR

This paper investigates the long-term behavior of coupled forward-backward stochastic differential equations with a parameter, establishing a large deviation principle to understand the probability of rare events in their solutions.

Contribution

It provides the first analysis of the asymptotic properties and large deviation principles for coupled FBSDEs with a parameter.

Findings

Established asymptotic behavior of solutions

Proved a large deviation principle for the processes

Characterized the probability of rare events in solutions

Abstract

In this paper, we consider coupled forward-backward stochastic differential equations (FBSDEs in short) with parameter $\varepsilon >0$. We study the asymptotic behavior of its solutions and establish a large deviation principle for the corresponding processes.