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

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

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.

Quanyan Zhu | Song Fang

[1] Quanyan Zhu,et al. Independent Elliptical Distributions Minimize Their W2 Wasserstein Distance from Independent Elliptical Distributions with the Same Density Generator , 2020, ArXiv.

[2] F. Santambrogio. Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling , 2015 .

[3] Michele Pavon,et al. Hellinger Versus Kullback–Leibler Multivariable Spectrum Approximation , 2007, IEEE Transactions on Automatic Control.

[4] Marco Cuturi,et al. Computational Optimal Transport: With Applications to Data Science , 2019 .

[5] G. Picci,et al. Linear Stochastic Systems: A Geometric Approach to Modeling, Estimation and Identification , 2016 .

[6] H. Araki. On an inequality of Lieb and Thirring , 1990 .

[7] Pedro M. Crespo,et al. Asymptotically Equivalent Sequences of Matrices and Hermitian Block Toeplitz Matrices With Continuous Symbols: Applications to MIMO Systems , 2008, IEEE Transactions on Information Theory.

[8] Yoav Zemel,et al. An Invitation to Statistics in Wasserstein Space , 2020 .

[9] C. Villani. Topics in Optimal Transportation , 2003 .

[10] Filippo Santambrogio,et al. Optimal Transport for Applied Mathematicians , 2015 .