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arXiv · 2404.04499

On the equivalence between Fourier-based and Wasserstein distances for probability measures on $\mathbb N$

Fei Cao·Xiaoqian Gong
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Abstract

In this manuscript we investigate the equivalence of Fourier-based metrics on discrete state spaces with the well-known Wasserstein distances. While the use of Fourier-based metrics in continuous state spaces is ubiquitous since its introduction by Giuseppe Toscani and his colleagues [9, 14, 16] in the study of kinetic-type partial differential equations, the introduction of its discrete analog is recent [2] and seems to be far less studied. In this work, various relations between Fourier-based metrics and Wasserstein distances are shown to hold when the state space is the set of non-negative integers $\mathbb N$. Lastly, we also describe potential applications of such equivalence of metrics in models from econophysics which motivate the present work.

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Fei Cao, Xiaoqian Gong. 2024-04-06. On the equivalence between Fourier-based and Wasserstein distances for probability measures on $\mathbb N$. https://arxiv.org/abs/2404.04499

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