{"title":"Spatial average for the solution to the heat equation with Rosenblatt noise","authors":"R. Dhoyer, C. Tudor","doi":"10.1080/07362994.2021.1972008","DOIUrl":null,"url":null,"abstract":"Abstract We consider the stochastic heat equation driven by a Rosenblatt sheet and we study the limit behavior in distribution of the spatial average of the solution. By analyzing the cumulants of the solution, we prove that the spatial average converges weakly, in the space of continuous functions, to a Rosenblatt process.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"40 1","pages":"951 - 966"},"PeriodicalIF":0.8000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/07362994.2021.1972008","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract We consider the stochastic heat equation driven by a Rosenblatt sheet and we study the limit behavior in distribution of the spatial average of the solution. By analyzing the cumulants of the solution, we prove that the spatial average converges weakly, in the space of continuous functions, to a Rosenblatt process.
期刊介绍：
Stochastic Analysis and Applications presents the latest innovations in the field of stochastic theory and its practical applications, as well as the full range of related approaches to analyzing systems under random excitation. In addition, it is the only publication that offers the broad, detailed coverage necessary for the interfield and intrafield fertilization of new concepts and ideas, providing the scientific community with a unique and highly useful service.
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