Limit Behavior of the Solution of Fractional Markovian Jump System Driven by Multiplicative Fractional Brownian Motion

This work is devoted to the analysis of the limit behavior of the solution to a class of fractional stochastic differential equations with Markovian switching and multiplicative fractional Brownian motion. With the aid of fractional calculus, generalized Riemann-Stieltjes integrals, stopping time techniques and inequality techniques, an averaging principle is established within the framework of Hölder continuous spaces. We prove that the solution of the original fractional Markovian jump system converges in the mean-square sense to that of the averaged equation, thereby justifying the averaging method as an effective technique for reducing the system’s complexity. Finally, concrete examples are presented to demonstrate our theoretical findings.