Large deviations for drift parameter estimator of mixed fractional Ornstein--Uhlenbeck process

TL;DR

This paper studies the probability of rare events in estimating the drift of a mixed fractional Ornstein-Uhlenbeck process, providing insights into the estimator's behavior under large deviations.

Contribution

It establishes large deviation principles for the maximum likelihood estimator of the drift parameter in a mixed fractional Ornstein-Uhlenbeck process.

Findings

Derived large deviation rate functions for the estimator.

Characterized the asymptotic probabilities of estimation errors.

Extended classical results to processes driven by mixed fractional Brownian motion.

Abstract

We investigate large deviation properties of the maximum likelihood drift parameter estimator for Ornstein--Uhlenbeck process driven by mixed fractional Brownian motion.