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

This is the published version, also available here: http://www.dx.doi.org/10.1214/12-AOP825.We prove a central limit theorem for an additive functional of the d-dimensional fractional Brownian motion with Hurst index H∈(11+d,1d), using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion