The Spectral-Domain $\mathcal{W}_2$ Wasserstein Distance for Elliptical Processes and the Spectral-Domain Gelbrich Bound
arXiv:2012.04023v2
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This work addresses theoretical gaps in comparing stochastic processes for researchers in probability theory and signal processing, but it is incremental as it extends existing concepts to the spectral domain.
The authors introduced a spectral-domain Wasserstein distance for elliptical stochastic processes based on power spectra and a spectral-domain Gelbrich bound for more general processes, providing mathematical formulations without specific numerical results.
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.