{"title":"The Burgers-type equation driven by a stochastic measure","authors":"Vadym Radchenko","doi":"10.1090/tpms/1213","DOIUrl":null,"url":null,"abstract":"We study the one-dimensional equation driven by a stochastic measure \n\n \n μ\n \\mu\n \n\n. For \n\n \n μ\n \\mu\n \n\n we assume only \n\n \n σ\n \\sigma\n \n\n-additivity in probability. Our results imply the global existence and uniqueness of the solution to the heat equation and the local existence and uniqueness of the solution to the Burgers equation. The averaging principle for such equation is studied.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and Mathematical Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tpms/1213","RegionNum":0,"RegionCategory":null,"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 study the one-dimensional equation driven by a stochastic measure
μ
\mu
. For
μ
\mu
we assume only
σ
\sigma
-additivity in probability. Our results imply the global existence and uniqueness of the solution to the heat equation and the local existence and uniqueness of the solution to the Burgers equation. The averaging principle for such equation is studied.
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