Cohen, Guyon, Perrin and Pontier have given assumptions under which the second-order quadratic variations of a Gaussian process converge almost surely to a deterministic limit. In this paper we present two new convergence results about these variations: the first is a deterministic asymptotic expansion; the second is a central limit theorem. Next we apply these results to identify two-parameter fractional Brownian motion and anisotropic fractional Brownian motion.
Publié le : 2007-08-14
Classification:
almost sure convergence,
central limit theorem,
fractional processes,
Gaussian processes,
generalized quadratic variations
@article{1186503484,
author = {Begyn, Arnaud},
title = {Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes},
journal = {Bernoulli},
volume = {13},
number = {1},
year = {2007},
pages = { 712-753},
language = {en},
url = {http://dml.mathdoc.fr/item/1186503484}
}
Begyn, Arnaud. Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes. Bernoulli, Tome 13 (2007) no. 1, pp. 712-753. http://gdmltest.u-ga.fr/item/1186503484/