@article{ECP1415,
author = {Jean-Christophe Breton and Ivan Nourdin},
title = {Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {13},
year = {2008},
keywords = {Total variation distance; Non-central limit theorem; Fractional Brownian motion; Hermite power variation; Multiple stochastic integrals; Hermite random variable},
abstract = {Let $q\geq 2$ be a positive integer, $B$ be a fractional Brownian motion with Hurst index $H\in(0,1)$, $Z$ be an Hermite random variable of index $q$, and $H_q$ denote the $q$th Hermite polynomial. For any $n\geq 1$, set $V_n=\sum_{k=0}^{n-1} H_q(B_{k+1}-B_k)$. The aim of the current paper is to derive, in the case when the Hurst index verifies $H>1-1/(2q)$, an upper bound for the total variation distance between the laws $\mathscr{L}(Z_n)$ and $\mathscr{L}(Z)$, where $Z_n$ stands for the correct renormalization of $V_n$ which converges in distribution towards $Z$. Our results should be compared with those obtained recently by Nourdin and Peccati (2007) in the case where $H<1-1/(2q)$, corresponding to the case where one has normal approximation.},
pages = {no. 46, 482-493},
issn = {1083-589X},
doi = {10.1214/ECP.v13-1415},
url = {http://ecp.ejpecp.org/article/view/1415}}