Local Asymptotic Normality for Mixed Fractional Brownian Motion with $0<H<3/4$

Chunhao Cai

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arXiv · 2512.24042

Local Asymptotic Normality for Mixed Fractional Brownian Motion with $0<H<3/4$

Chunhao Cai

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Abstract

This paper establishes the Local Asymptotic Normality (LAN) property for the mixed fractional Brownian motion under high-frequency observations with Hurst index $H \in (0, 3/4)$. The simultaneous estimation of the volatility and the Hurst index encounters a degeneracy problem in the Fisher information matrix.

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Chunhao Cai. 2025-12-30. Local Asymptotic Normality for Mixed Fractional Brownian Motion with $0<H<3/4$. https://arxiv.org/abs/2512.24042

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