Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes

Details Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes

2007-09-05

arxiv.org/abs/0709.0598v1

Bernoulli 2007, Vol. 13, No. 3, 712-753

Mathematics

Probability

Published at http://dx.doi.org/10.3150/07-BEJ5112 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ5112

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.

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