In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q≥2 of the fractional Brownian motion with Hurst parameter H∈(0, 1), where q is an integer. The central limit holds for 1/2q2 to a limit which only depends on the fractional Brownian motion, and if H>1−1/2q we show the convergence in L2 to a stochastic integral with respect to the Hermite process of order q.
Publié le : 2010-11-15
Classification:
Fractional Brownian motion,
Central limit theorem,
Non-central limit theorem,
Hermite process,
60F05,
60H05,
60G15,
60H07
@article{1288878338,
author = {Nourdin, Ivan and Nualart, David and Tudor, Ciprian A.},
title = {Central and non-central limit theorems for weighted power variations of fractional Brownian motion},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 1055-1079},
language = {en},
url = {http://dml.mathdoc.fr/item/1288878338}
}
Nourdin, Ivan; Nualart, David; Tudor, Ciprian A. Central and non-central limit theorems for weighted power variations of fractional Brownian motion. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 1055-1079. http://gdmltest.u-ga.fr/item/1288878338/