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

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.

arXiv commentPublished 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)

References in corpus (2)

• Renormalized self-intersection local time for fractional Brownian motion
• Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case $H=1/4$