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.
"Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes." Bernoulli 13 (3) 712 - 753, August 2007. https://doi.org/10.3150/07-BEJ5112