Rate of convergence for the weighted Hermite variations of the fractional Brownian motion

Abstract

In this paper we obtain a rate of convergence in the central limit theorem for high order weighted Hermite variations of the fractional Brownian motion. The proof is based on the techniques of Malliavin calculus and the quantitative stable limit theorems proved by Nourdin, Nualart and Peccati in 2016.

arXiv comment25 pages

References in corpus (4)

• Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion
• Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: The critical case $H=1/4$
• Quantitative stable limit theorems on the Wiener space
• Total variation estimates in the Breuer-Major theorem