Limit theorems for functions of stationary mean-zero Gaussian sequences of vectors satisfying long range dependence conditions are considered. Depending on the rate of decay of the coefficients, the limit law can be either Gaussian or the law of a multiple Ito-Wiener integral. We prove the bootstrap of these limit theorems in the case when the limit is normal. A sufficient bracketing condition for these limit theorems to happen uniformly over a class of functions is presented.
Publié le : 1994-10-14
Classification:
Long range dependence,
bootstrap,
multiple Ito-Wiener integrals,
moving blocks bootstrap,
empirical processes,
stationary Gaussian sequence,
60F05,
60F17,
60G10
@article{1176988503,
author = {Arcones, Miguel A.},
title = {Limit Theorems for Nonlinear Functionals of a Stationary Gaussian Sequence of Vectors},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 2242-2274},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988503}
}
Arcones, Miguel A. Limit Theorems for Nonlinear Functionals of a Stationary Gaussian Sequence of Vectors. Ann. Probab., Tome 22 (1994) no. 4, pp. 2242-2274. http://gdmltest.u-ga.fr/item/1176988503/