The Annals of Probability

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

Yaozhong Hu, David Nualart, and Fangjun Xu

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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 the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.

Article information

Ann. Probab., Volume 42, Number 1 (2014), 168-203.

First available in Project Euclid: 9 January 2014

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G22: Fractional processes, including fractional Brownian motion

Fractional Brownian motion central limit theorem local time method of moments


Hu, Yaozhong; Nualart, David; Xu, Fangjun. Central limit theorem for an additive functional of the fractional Brownian motion. Ann. Probab. 42 (2014), no. 1, 168--203. doi:10.1214/12-AOP825.

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