• Bernoulli
  • Volume 13, Number 3 (2007), 712-753.

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

Arnaud Begyn

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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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Bernoulli, Volume 13, Number 3 (2007), 712-753.

First available in Project Euclid: 7 August 2007

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almost sure convergence central limit theorem fractional processes Gaussian processes generalized quadratic variations


Begyn, Arnaud. Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes. Bernoulli 13 (2007), no. 3, 712--753. doi:10.3150/07-BEJ5112.

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