Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes
arXiv:0709.0598 · doi:10.3150/07-BEJ5112
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.
Published at http://dx.doi.org/10.3150/07-BEJ5112 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)