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

Yaozhong Hu; David Nualart; Fangjun Xu

doi:10.1214/12-AOP825

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

Probability 2014-01-15 v2

Authors: 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.

Keywords

fractional Brownian motion additive functional central limit theorem method of moments Hurst index

Cite

@article{arxiv.1111.4419,
  title  = {Central limit theorem for an additive functional of the fractional Brownian motion},
  author = {Yaozhong Hu and David Nualart and Fangjun Xu},
  journal= {arXiv preprint arXiv:1111.4419},
  year   = {2014}
}

Comments

Published in at http://dx.doi.org/10.1214/12-AOP825 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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