Local asymptotic normality for mixed fractional Ornstein-Uhlenbeck process under high-frequency observation

TL;DR

This paper establishes the local asymptotic normality (LAN) property for a mixed fractional Ornstein-Uhlenbeck process observed at high frequency when the Hurst parameter exceeds 3/4, extending existing results in fractional stochastic processes.

Contribution

It introduces the LAN property for the mixed fractional Ornstein-Uhlenbeck process under high-frequency observations for H>3/4, utilizing a projection step to handle the non-diagonal rate matrix.

Findings

Proves LAN property for H>3/4 in mixed fractional OU process.

Uses projection step to derive non-diagonal rate matrix.

Extends fractional Brownian motion analysis to mixed processes.

Abstract

This paper consider the LAN property for the mixed O-U process under high-frequency observation when H>3/4. As considered in mixed fractional Brownian motion, we will also use the projection step to get the non-diagonal rate matrix.