{"title":"Stochastic parallel translations and diffusions on the Wasserstein space over T","authors":"Hao Ding , Shizan Fang , Xiang-Dong Li","doi":"10.1016/j.spa.2025.104602","DOIUrl":null,"url":null,"abstract":"<div><div>We establish the existence and uniqueness of stochastic parallel translations and diffusions driven by a Q-Wiener process on the Wasserstein space over <span><math><mi>T</mi></math></span>. Surprisingly enough, the equation defining stochastic parallel translations is a SDE on a Hilbert space, instead of a SPDE.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"184 ","pages":"Article 104602"},"PeriodicalIF":1.1000,"publicationDate":"2025-02-11","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/S0304414925000432","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
We establish the existence and uniqueness of stochastic parallel translations and diffusions driven by a Q-Wiener process on the Wasserstein space over . Surprisingly enough, the equation defining stochastic parallel translations is a SDE on a Hilbert space, instead of a SPDE.
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.
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