Gaussian random fields

Abstract

After some general results relating mixing properties of a Gaussian random field, we propose an explicit bound of the mixing coefficients of such a random field based on the approximation properties of its spectral density in § 2.1.1. In § 2.1.2. more precise results characterize the decay of such coefficients for Gaussian processes. In this chapter, X = (X_t)_t∈T denotes a stationary Gaussian random field indexed by some metric group T.