{"title":"带有加性噪声的随机热方程的概率一命中率","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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-06-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10959-024-01342-4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10959-024-01342-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hitting with Probability One for Stochastic Heat Equations with Additive Noise
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.
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