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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2404.04499 |
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| _version_ | 1866929304078647296 |
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| author | Cao, Fei Gong, Xiaoqian |
| author_facet | Cao, Fei Gong, Xiaoqian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the equivalence between Fourier-based and Wasserstein distances for probability measures on $\mathbb N$ Cao, Fei Gong, Xiaoqian Probability 91B70, 91B80 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. |
| title | On the equivalence between Fourier-based and Wasserstein distances for probability measures on $\mathbb N$ |
| topic | Probability 91B70, 91B80 |
| url | https://arxiv.org/abs/2404.04499 |