The Spectral-Domain ${\mathcal{W}}_2$ Wasserstein Distance for Elliptical Processes and the Spectral-Domain Gelbrich Bound

Abstract

In this short note, we introduce the spectral-domain ${\mathcal{W}}_2$ Wasserstein distance for elliptical stochastic processes in terms of their power spectra. We also introduce the spectral-domain Gelbrich bound for processes that are not necessarily elliptical.