Moderate deviation principle for multiscale systems driven by fractional Brownian motion

. 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 ∈ (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.

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