{"title":"平稳随机测度间传输距离的Benamou-Brenier公式","authors":"Martin Huesmann, Bastian Müller","doi":"10.1016/j.spa.2025.104633","DOIUrl":null,"url":null,"abstract":"<div><div>We derive a Benamou–Brenier type dynamical formulation for the Kantorovich–Wasserstein extended metric <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> between stationary random measures recently introduced in Erbar et al., (2024). A key step is a reformulation of the extended metric <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> using Palm probabilities.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"185 ","pages":"Article 104633"},"PeriodicalIF":1.1000,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Benamou–Brenier formula for transport distances between stationary random measures\",\"authors\":\"Martin Huesmann, Bastian Müller\",\"doi\":\"10.1016/j.spa.2025.104633\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We derive a Benamou–Brenier type dynamical formulation for the Kantorovich–Wasserstein extended metric <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> between stationary random measures recently introduced in Erbar et al., (2024). A key step is a reformulation of the extended metric <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> using Palm probabilities.</div></div>\",\"PeriodicalId\":51160,\"journal\":{\"name\":\"Stochastic Processes and their Applications\",\"volume\":\"185 \",\"pages\":\"Article 104633\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2025-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Stochastic Processes and their Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0304414925000742\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Processes and their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304414925000742","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
A Benamou–Brenier formula for transport distances between stationary random measures
We derive a Benamou–Brenier type dynamical formulation for the Kantorovich–Wasserstein extended metric between stationary random measures recently introduced in Erbar et al., (2024). A key step is a reformulation of the extended metric using Palm probabilities.
期刊介绍:
Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests.
Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.