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

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.

the proofs are only valid for H<5/8. There are some mistakes of proofs in this manuscript