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

TL;DR

This paper establishes a central limit theorem for additive functionals of multi-dimensional fractional Brownian motion with specific Hurst indices, extending classical results from standard Brownian motion to fractional cases.

Contribution

It extends the central limit theorem for additive functionals from standard Brownian motion to fractional Brownian motion with certain Hurst indices, using the method of moments.

Findings

Proves a CLT for fractional Brownian motion with H in (1/(2+d), 1/d)

Extends classical CLT results to fractional case

Uses method of moments for proof

Abstract

We prove a central limit theorem for an additive functional of the $d$-dimensional fractional Brownian motion with Hurst index $H\in(\frac{1}{2+d},\frac{1}{d})$, using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.