Probabilistic Analysis of Distributed Fractional-Order Stochastic Systems Driven by Fractional Brownian Motion: Existence, Uniqueness, and Transportation Inequalities

This paper investigates a class of distributed fractional-order stochastic differential equations driven by fractional Brownian motion with a Hurst parameter 1/2<H<1. By employing the Picard iteration method, we rigorously prove the existence and uniqueness of solutions with Lipschitz conditions. Furthermore, leveraging the Girsanov transformation argument within the L2 metric framework, we derive quadratic transportation inequalities for the law of the strong solution to the considered equations. These results provide a deeper understanding of the regularity and probabilistic properties of the solutions in this framework.