Central limit theorem for functionals of two independent fractional Brownian motions

TL;DR

This paper establishes a central limit theorem for functionals of two independent fractional Brownian motions with the same Hurst index, expanding understanding of their probabilistic behavior in specific Hurst index ranges.

Contribution

It introduces a new CLT for functionals of two independent fractional Brownian motions within a specific Hurst index range, using the method of moments.

Findings

Proves a CLT for functionals of two independent fractional Brownian motions.

Identifies the Hurst index range $(\frac{2}{d+1},\frac{2}{d})$ where the theorem applies.

Uses the method of moments to establish the result.

Abstract

We prove a central limit theorem for functionals of two independent $d$-dimensional fractional Brownian motions with the same Hurst index $H$ in $(\frac{2}{d+1},\frac{2}{d})$ using the method of moments.