Asymptotically Efficient Estimation of Ergodic Rough Fractional Ornstein-Uhlenbeck Process under Continuous Observations

TL;DR

This paper develops efficient methods for estimating drift parameters of an ergodic fractional Ornstein-Uhlenbeck process with Hurst parameter less than 1/2, under continuous observations, providing optimal rates and variances.

Contribution

It introduces asymptotically efficient estimators for drift parameters of the process, including proving the efficiency of the maximum likelihood estimator.

Findings

Derived asymptotic rates and variances for estimators.

Proved the asymptotic efficiency of the maximum likelihood estimator.

Focused on processes with non-zero stationary mean and H<1/2.

Abstract

We consider the problem of asymptotically efficient estimation of drift parameters of the ergodic fractional Ornstein-Uhlenbeck process under continuous observations when the Hurst parameter $H<1/2$ and the mean of its stationary distribution is not equal to zero. In this paper, we derive asymptotically efficient rates and variances of estimators of drift parameters and prove an asymptotic efficiency of a maximum likelihood estimator of drift parameters.