Sharp large deviations for the fractional Ornstein-Uhlenbeck process

TL;DR

This paper studies the precise probabilities of rare events for the energy and estimator of a fractional Ornstein-Uhlenbeck process driven by fractional Brownian motion with Hurst index > 0.5.

Contribution

It provides new sharp large deviation results for key statistical quantities of the fractional Ornstein-Uhlenbeck process, extending classical theory.

Findings

Derived explicit large deviation rate functions.

Established asymptotic behaviors of the energy and estimator.

Enhanced understanding of rare event probabilities in fractional stochastic processes.

Abstract

We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst index greater than one half.