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 ∈ (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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