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

preprint2025arXivOpen access

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

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