{"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":"<div><p>We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝ<sup><i>d</i></sup> with <i>d</i> ≥ 1 and show that, even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on ℝ<sup><i>d</i></sup>, their local times exist when <i>d</i> ≤ 3. A Tanaka formula of the local time is also derived.</p></div>","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\":\"<div><p>We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝ<sup><i>d</i></sup> with <i>d</i> ≥ 1 and show that, even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on ℝ<sup><i>d</i></sup>, their local times exist when <i>d</i> ≤ 3. A Tanaka formula of the local time is also derived.</p></div>\",\"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://link.springer.com/article/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://link.springer.com/article/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}
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 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.
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.
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