A Note On Inference for the Mixed Fractional Ornstein-Uhlenbeck Process with Drift

TL;DR

This paper investigates the parameter estimation for the mixed fractional Ornstein-Uhlenbeck process with drift, deriving large sample properties of the maximum likelihood estimator using advanced probabilistic techniques.

Contribution

It provides new asymptotic results for the maximum likelihood estimator of the process parameters, extending previous work with additional mathematical tools.

Findings

Asymptotic normality of the MLE established

Explicit expressions for the Laplace transform used

Enhanced understanding of inference in fractional processes

Abstract

This paper is devoted to parameter estimation of the mixed fractional Ornstein-Uhlenbeck process with a drift. Large sample asymptotical properties of the Maximum Likelihood Estimator is deduced using the Laplace transform computations or the Cameron-Martin formula with extra part from \cite{CK19}