A Simple Proof of Berry-Esséen Bounds for the Quadratic Variation of the Subfractional Brownian Motion

Soufiane Aazizi

Published 2012-07-24Version 1

We give a simple technic to derive the Berry-Ess\'een bounds for the quadratic variation of the subfractional Brownian motion (subfBm). Our approach has two main ingredients: ($i$) bounding from above the covariance of quadratic variation of subfBm by the covariance of the quadratic variation of fractional Brownian motion (fBm); and ($ii$) using the existing results on fBm in \cite{BN08,NP09,N12}. As a result, we obtain simple and direct proof to derive the rate of convergence of quadratic variation of subfBm. In addition, we also improve this rate of convergence to meet the one of fractional Brownian motion in \cite{N12}.