{"title":"Energy of taut strings accompanying random walk","authors":"M. Lifshits, A. Siuniaev","doi":"10.37190/0208-4147.41.1.2","DOIUrl":null,"url":null,"abstract":"We consider the kinetic energy of the taut strings accompanying trajectories of a Wiener process and a random walk. Under certain assumptions on the band width, it is shown that the energy of a taut string accompanying a random walk within a band satisfies the same strong law of large numbers as proved earlier for a Wiener process and a fixed band width. New results for Wiener processes are also obtained. 2020 Mathematics Subject Classification: Primary 60G15; Secondary 60G17, 60F15.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":"1 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability and Mathematical Statistics-Poland","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.37190/0208-4147.41.1.2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the kinetic energy of the taut strings accompanying trajectories of a Wiener process and a random walk. Under certain assumptions on the band width, it is shown that the energy of a taut string accompanying a random walk within a band satisfies the same strong law of large numbers as proved earlier for a Wiener process and a fixed band width. New results for Wiener processes are also obtained. 2020 Mathematics Subject Classification: Primary 60G15; Secondary 60G17, 60F15.
期刊介绍：
PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.
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