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We prove a central limit theorem for an additive functional of the$d$-dimensional fractional Brownian motion with Hurst index$H\in(\frac{1}{1+d},\frac{1}{d})$, using the method of moments, extending theresult by Papanicolaou, Stroock and Varadhan in the case of the standardBrownian motion.

Central limit theorem for an additive functional of the fractional Brownian motion