{"title":"A functional modulus of continuity for Brownian motion","authors":"Jicheng Liu , Jiagang Ren","doi":"10.1016/j.bulsci.2006.03.009","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we prove a sharpening of large deviation for increments of Brownian motion in <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>r</mi><mo>)</mo></math></span>-capacity and Hölder norm case. As an application, we obtain a functional modulus of continuity for <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>r</mi><mo>)</mo></math></span>-capacity in the stronger topology.</p></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"131 1","pages":"Pages 60-71"},"PeriodicalIF":0.9000,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.bulsci.2006.03.009","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin des Sciences Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0007449706000376","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 4
Abstract
In this paper, we prove a sharpening of large deviation for increments of Brownian motion in -capacity and Hölder norm case. As an application, we obtain a functional modulus of continuity for -capacity in the stronger topology.
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