Spectral Conditions for Equivalence of Gaussian Random Fields with Stationary Increments

TL;DR

This paper establishes spectral conditions under which Gaussian random fields with stationary increments are equivalent, extending previous results and applicable to complex nonstationary space-time models with anisotropy.

Contribution

It provides a new sufficient spectral condition for the equivalence of Gaussian measures induced by nonstationary Gaussian random fields with stationary increments.

Findings

Proves a spectral condition for measure equivalence at infinity.

Extends prior results to nonstationary, anisotropic space-time models.

Applicable to a broad class of nonstationary Gaussian fields.

Abstract

This paper studies the problem of equivalence of Gaussian measures induced by Gaussian random fields (GRFs) with stationary increments and proves a sufficient condition for the equivalence in terms of the behavior of the spectral measures at infinity. The main results extend those of Stein (2004), Van Zanten (2007, 2008) and are applicable to a rich family of nonstationary space-time models with possible anisotropy behavior.