Moderate Deviation Principle for Multiscale Systems Driven by Fractional Brownian Motion

Abstract

In this paper, we study the moderate deviations principle (MDP) for slow–fast stochastic dynamical systems where the slow motion is governed by small fractional Brownian motion (fBm) with Hurst parameter \(H\in (1/2,1)\). We derive conditions on the moderate deviations scaling and on the Hurst parameter H under which the MDP holds. In addition, we show that in typical situations the resulting action functional is discontinuous in H at \(H=1/2\), suggesting that the tail behavior of stochastic dynamical systems perturbed by fBm can have different characteristics than the tail behavior of such systems that are perturbed by standard Brownian motion.