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arXiv · 1111.4419

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

Yaozhong Hu·David Nualart·Fangjun Xu
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Abstract

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.

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Yaozhong Hu, David Nualart, Fangjun Xu. 2011-11-18. Central limit theorem for an additive functional of the fractional Brownian motion. https://doi.org/10.1214/12-aop825

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