含Rosenblatt噪声的热方程解的空间平均

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications Pub Date : 2021-11-01 DOI:10.1080/07362994.2021.1972008

R. Dhoyer, C. Tudor

{"title":"含Rosenblatt噪声的热方程解的空间平均","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":"{\"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}","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

摘要

摘要考虑Rosenblatt薄板驱动的随机热方程，研究了其解的空间平均分布的极限行为。通过分析解的累积量，证明了空间平均在连续函数空间弱收敛于Rosenblatt过程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Spatial average for the solution to the heat equation with Rosenblatt noise

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Stochastic Analysis and Applications 数学-统计学与概率论

CiteScore

2.70

自引率

7.70%

发文量

审稿时长

6-12 weeks

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.