Adapted optimal transport between Gaussian processes in discrete time
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909454742585344 |
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| author | Gunasingam, Madhu Wong, Ting-Kam Leonard |
| author_facet | Gunasingam, Madhu Wong, Ting-Kam Leonard |
| contents | We derive explicitly the adapted $2$-Wasserstein distance between non-degenerate Gaussian distributions on $\mathbb{R}^N$ and characterize the optimal bicausal coupling(s). This leads to an adapted version of the Bures-Wasserstein distance on the space of positive definite matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adapted optimal transport between Gaussian processes in discrete time Gunasingam, Madhu Wong, Ting-Kam Leonard Probability 49Q22, 60G15 (Primary), 60B10 (Secondary) We derive explicitly the adapted $2$-Wasserstein distance between non-degenerate Gaussian distributions on $\mathbb{R}^N$ and characterize the optimal bicausal coupling(s). This leads to an adapted version of the Bures-Wasserstein distance on the space of positive definite matrices. |
| title | Adapted optimal transport between Gaussian processes in discrete time |
| topic | Probability 49Q22, 60G15 (Primary), 60B10 (Secondary) |
| url | https://arxiv.org/abs/2404.06625 |