一类相互作用的分支量值扩散的田中公式和局部时间

IF 0.8 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2023-12-08 DOI:10.1007/s10114-023-2308-2

Donald A. Dawson, Jean Vaillancourt, Hao Wang

{"title":"一类相互作用的分支量值扩散的田中公式和局部时间","authors":"Donald A. Dawson, Jean Vaillancourt, Hao Wang","doi":"10.1007/s10114-023-2308-2","DOIUrl":null,"url":null,"abstract":"We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝd with d ≥ 1 and show that, even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on ℝd, their local times exist when d ≤ 3. A Tanaka formula of the local time is also derived.","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions\",\"authors\":\"Donald A. Dawson, Jean Vaillancourt, Hao Wang\",\"doi\":\"10.1007/s10114-023-2308-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝd with d ≥ 1 and show that, even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on ℝd, their local times exist when d ≤ 3. A Tanaka formula of the local time is also derived.\",\"PeriodicalId\":50893,\"journal\":{\"name\":\"Acta Mathematica Sinica-English Series\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-12-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Sinica-English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10114-023-2308-2\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10114-023-2308-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们构建了欧几里得空间ℝd中d≥1的依赖空间运动的超过程（SDSM），并证明了即使它们从某些无界的初始正Radon度量（如ℝd上的Lebesgue度量）开始，当d≤3时，它们的局部时间也是存在的。同时还推导出了局部时间的田中公式。

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

Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions

We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝ^d with d ≥ 1 and show that, even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on ℝ^d, their local times exist when d ≤ 3. A Tanaka formula of the local time is also derived.

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

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.