{"title":"Hitting with Probability One for Stochastic Heat Equations with Additive Noise","authors":"Robert C. Dalang, Fei Pu","doi":"10.1007/s10959-024-01342-4","DOIUrl":null,"url":null,"abstract":"<p>We study the hitting probabilities of the solution to a system of <i>d</i> stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive <span>\\((d-6)\\)</span>-dimensional capacity, the solution visits this set almost surely.</p>","PeriodicalId":54760,"journal":{"name":"Journal of Theoretical Probability","volume":"44 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Theoretical Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10959-024-01342-4","RegionNum":4,"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 study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive \((d-6)\)-dimensional capacity, the solution visits this set almost surely.
期刊介绍：
Journal of Theoretical Probability publishes high-quality, original papers in all areas of probability theory, including probability on semigroups, groups, vector spaces, other abstract structures, and random matrices. This multidisciplinary quarterly provides mathematicians and researchers in physics, engineering, statistics, financial mathematics, and computer science with a peer-reviewed forum for the exchange of vital ideas in the field of theoretical probability.
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