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

Chunhao Cai; Cong Zhang

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arXiv · 2510.17233

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

Chunhao Cai·Cong Zhang

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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 $H>3/4$.

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Chunhao Cai, Cong Zhang. 2025-10-20. LAN Property for the Drift and Hurst Paramters in The Mixed Fractional O-U Process with Continuous Observations. https://arxiv.org/abs/2510.17233

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