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

Arnaud Begyn

doi:10.3150/07-bej5112

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arXiv · 0709.0598

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

Arnaud Begyn

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Abstract

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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Arnaud Begyn. 2007-09-05. Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes. https://doi.org/10.3150/07-bej5112

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