Fully Coupled Forward-backward Stochastic Differential Equations on Markov Chains

TL;DR

This paper introduces a new class of stochastic differential equations on Markov Chain spaces, establishing their existence and uniqueness, which advances the mathematical understanding of stochastic processes in discrete state spaces.

Contribution

It defines fully coupled forward-backward stochastic differential equations on Markov Chains and proves their existence and uniqueness, a novel extension in stochastic analysis.

Findings

Existence of solutions established

Uniqueness of solutions proven

Framework for future stochastic process analysis on Markov Chains

Abstract

We define fully coupled forward-backward stochastic differential equations on spaces related to continuous time, finite state Markov Chains. Existence and uniqueness results of the fully coupled forward-backward stochastic differential equations on Markov Chains are obtained.