Moderate deviation principle for multiscale systems driven by fractional Brownian motion

TL;DR

This paper establishes a moderate deviations principle for multiscale stochastic systems driven by fractional Brownian motion with Hurst parameter greater than 1/2, highlighting the impact of H on tail behavior.

Contribution

It derives conditions under which the MDP holds for systems driven by fractional Brownian motion and reveals discontinuities at H=1/2 affecting tail behavior.

Findings

MDP holds under specific scaling and Hurst parameter conditions

Action functional is discontinuous at H=1/2

Tail behavior differs from standard Brownian motion cases

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.