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We give a simple technic to derive the Berry-Ess\'een bounds for thequadratic variation of the subfractional Brownian motion (subfBm). Our approachhas two main ingredients: ($i$) bounding from above the covariance of quadraticvariation of subfBm by the covariance of the quadratic variation of fractionalBrownian 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 derivethe rate of convergence of quadratic variation of subfBm. In addition, we alsoimprove this rate of convergence to meet the one of fractional Brownian motionin \cite{N12}.

A Simple Proof of Berry-Ess\'een Bounds for the Quadratic Variation of the Subfractional Brownian Motion