LAN Property for the Drift and Hurst Paramters in The Mixed Fractional O-U Process with Continuous Observations

TL;DR

This paper establishes the local asymptotic normality for joint estimation of drift and Hurst parameters in a mixed fractional Ornstein-Uhlenbeck process with continuous observations, specifically for Hurst parameter H>3/4.

Contribution

It introduces a novel approach for joint parameter estimation in the mixed fractional OU process when H>3/4, leveraging the semimartingale property of the fractional Brownian motion.

Findings

Proves local asymptotic normality for joint parameters

Develops filtering techniques for H>3/4

Provides estimation methods for drift and Hurst parameters

Abstract

This paper deals with the Local Asymptotical normality for the joint drift parameter and Hurst parameter $H>3/4$ in the mixed fractional Ornstein-Uhlenbeck process. Different from the only estimation of the drift parameter when $H$ is known, we will use the fact that the mixed fractional Brownian motion is a semimartingale with its own filtering when $H>3/4$.