Limiting distribution of the continuity modulus for Gaussian processes with stationary increments

Abstract

Let {X(t), t is an element of R} be a Gaussian process with stationary increments, zero mean and a.s. continuous paths, whose variogram gamma(t) behaves like c vertical bar t vertical bar(alpha), c > 0, alpha, is an element of (0, 2), as t -> 0. We show that the continuity modulus of X has asymptotically Gumbel distribution. In the case alpha = 2, a non-Gumbel limiting distribution is obtained. (c) 2008 Elsevier B.V. All rights reserved.