Local Asymptotic Normality for Mixed Fractional Brownian Motion with $H>3/4$ Under High-Frequency Observation

Abstract: In this paper we will consider the LAN property for both the Hurst parameter $H>3/4$ and the variance of the fractional Brownian motion plus an independent standard Brownian motion (called mixed fractional Brownian motion) with high-frequency observation. We will first remove the $H$-score linear term and orthogonalize the remainder through two non-diagonal transformations, then we can construct the CLT for the quadratic form base on $| \cdot |_{\mathrm{op}}/|\cdot|_F\to0$. At last we obtain a diagonal Gaussian LAN expansion with an explicit information matrix.