{"title":"马尔可夫过程经验测度的Wasserstein收敛率","authors":"Feng-Yu Wang","doi":"10.1007/s00245-025-10275-1","DOIUrl":null,"url":null,"abstract":"<div><p>The convergence rate in Wasserstein distance is estimated for empirical measures of ergodic Markov processes, and the estimate can be sharp in some specific situations. The main result is applied to subordinations of typical models excluded by existing results, which include: stochastic Hamiltonian systems on <span>\\({\\mathbb{R}}^{n}\\times {\\mathbb{R}}^{m}\\)</span>, spherical velocity Langevin processes on <span>\\({\\mathbb{R}}^n\\times \\mathbb S^{n-1},\\)</span> multi-dimensional Wright–Fisher type diffusion processes, and stable type jump processes.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Wasserstein Convergence Rate for Empirical Measures of Markov Processes\",\"authors\":\"Feng-Yu Wang\",\"doi\":\"10.1007/s00245-025-10275-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The convergence rate in Wasserstein distance is estimated for empirical measures of ergodic Markov processes, and the estimate can be sharp in some specific situations. The main result is applied to subordinations of typical models excluded by existing results, which include: stochastic Hamiltonian systems on <span>\\\\({\\\\mathbb{R}}^{n}\\\\times {\\\\mathbb{R}}^{m}\\\\)</span>, spherical velocity Langevin processes on <span>\\\\({\\\\mathbb{R}}^n\\\\times \\\\mathbb S^{n-1},\\\\)</span> multi-dimensional Wright–Fisher type diffusion processes, and stable type jump processes.</p></div>\",\"PeriodicalId\":55566,\"journal\":{\"name\":\"Applied Mathematics and Optimization\",\"volume\":\"92 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics and Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00245-025-10275-1\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Optimization","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00245-025-10275-1","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Wasserstein Convergence Rate for Empirical Measures of Markov Processes
The convergence rate in Wasserstein distance is estimated for empirical measures of ergodic Markov processes, and the estimate can be sharp in some specific situations. The main result is applied to subordinations of typical models excluded by existing results, which include: stochastic Hamiltonian systems on \({\mathbb{R}}^{n}\times {\mathbb{R}}^{m}\), spherical velocity Langevin processes on \({\mathbb{R}}^n\times \mathbb S^{n-1},\) multi-dimensional Wright–Fisher type diffusion processes, and stable type jump processes.
期刊介绍:
The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.