{"citation":{"ama":"Abdellatif M, Kuchling P, Rüdiger B, Ventura I. Wasserstein distance in terms of the comonotonicity copula. <i>Stochastics</i>. 2024:1-12. doi:<a href=\"https://doi.org/10.1080/17442508.2024.2427734\">10.1080/17442508.2024.2427734</a>","ieee":"M. Abdellatif, P. Kuchling, B. Rüdiger, and I. Ventura, “Wasserstein distance in terms of the comonotonicity copula,” <i>Stochastics</i>, pp. 1–12, 2024.","mla":"Abdellatif, Mariem, et al. “Wasserstein Distance in Terms of the Comonotonicity Copula.” <i>Stochastics</i>, Informa UK Limited, 2024, pp. 1–12, doi:<a href=\"https://doi.org/10.1080/17442508.2024.2427734\">10.1080/17442508.2024.2427734</a>.","apa":"Abdellatif, M., Kuchling, P., Rüdiger, B., &#38; Ventura, I. (2024). Wasserstein distance in terms of the comonotonicity copula. <i>Stochastics</i>, 1–12. <a href=\"https://doi.org/10.1080/17442508.2024.2427734\">https://doi.org/10.1080/17442508.2024.2427734</a>","alphadin":"<span style=\"font-variant:small-caps;\">Abdellatif, Mariem</span> ; <span style=\"font-variant:small-caps;\">Kuchling, Peter</span> ; <span style=\"font-variant:small-caps;\">Rüdiger, Barbara</span> ; <span style=\"font-variant:small-caps;\">Ventura, Irene</span>: Wasserstein distance in terms of the comonotonicity copula. In: <i>Stochastics</i>, Informa UK Limited (2024), S. 1–12","chicago":"Abdellatif, Mariem, Peter Kuchling, Barbara Rüdiger, and Irene Ventura. “Wasserstein Distance in Terms of the Comonotonicity Copula.” <i>Stochastics</i>, 2024, 1–12. <a href=\"https://doi.org/10.1080/17442508.2024.2427734\">https://doi.org/10.1080/17442508.2024.2427734</a>.","bibtex":"@article{Abdellatif_Kuchling_Rüdiger_Ventura_2024, title={Wasserstein distance in terms of the comonotonicity copula}, DOI={<a href=\"https://doi.org/10.1080/17442508.2024.2427734\">10.1080/17442508.2024.2427734</a>}, journal={Stochastics}, publisher={Informa UK Limited}, author={Abdellatif, Mariem and Kuchling, Peter and Rüdiger, Barbara and Ventura, Irene}, year={2024}, pages={1–12} }","short":"M. Abdellatif, P. Kuchling, B. Rüdiger, I. Ventura, Stochastics (2024) 1–12."},"_id":"5134","abstract":[{"text":"The aim of this article is to write the p-Wasserstein metric 𝑊𝑝 with the p-norm, 𝑝∈[1,∞), on ℝ𝑑 in terms of copula. In particular for the case of one-dimensional distributions, we get that the copula employed to get the optimal coupling of the Wasserstein distances is the comotonicity copula. We obtain the equivalent result also for d-dimensional distributions under the sufficient and necessary condition that these have the same dependence structure of their one-dimensional marginals, i.e that the d-dimensional distributions share the same copula. Assuming 𝑝≠𝑞, p,q ∈[1,∞) and that the probability measures µ and ν are sharing the same copula, we also analyze the Wasserstein distance 𝑊𝑝,𝑞 discussed in [Alfonsi and Jourdain. A remark on the optimal transport between two probability measures sharing the same copula. Statist. Probab. Lett. 84 (2014) 131–134.] and get an upper and lower bounds of 𝑊𝑝,𝑞 in terms of 𝑊𝑝, written in terms of comonotonicity copula. We show that as a consequence the lower and upper bound of 𝑊𝑝,𝑞 can be written in terms of generalized inverse functions.","lang":"eng"}],"title":"Wasserstein distance in terms of the comonotonicity copula","language":[{"iso":"eng"}],"date_created":"2024-11-20T03:03:18Z","alternative_id":["5135","5136"],"user_id":"220548","publication_status":"published","doi":"10.1080/17442508.2024.2427734","status":"public","publication_identifier":{"eissn":["1744-2516"],"issn":["1744-2508"]},"date_updated":"2024-11-22T14:06:48Z","type":"journal_article","author":[{"full_name":"Abdellatif, Mariem","first_name":"Mariem","last_name":"Abdellatif"},{"orcid_put_code_url":"https://api.orcid.org/v2.0/0000-0002-8241-4076/work/172285511","last_name":"Kuchling","first_name":"Peter","orcid":"0000-0002-8241-4076","full_name":"Kuchling, Peter","id":"253182"},{"first_name":"Barbara","last_name":"Rüdiger","full_name":"Rüdiger, Barbara"},{"full_name":"Ventura, Irene","first_name":"Irene","last_name":"Ventura"}],"year":"2024","publication":"Stochastics","publisher":"Informa UK Limited","page":"1-12"}