广义线性多重分形稳定片：局部时间的存在性和联合连续性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-06-24 DOI:10.3150/22-bej1479

Yujia Ding, Qidi Peng, Yimin Xiao

{"title":"广义线性多重分形稳定片：局部时间的存在性和联合连续性","authors":"Yujia Ding, Qidi Peng, Yimin Xiao","doi":"10.3150/22-bej1479","DOIUrl":null,"url":null,"abstract":"We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) with α ∈ (0 , 2] , to include both linear multifractional Brownian sheets ( α = 2 ) and linear multifractional stable sheets ( α < 2 ). The purpose of the present paper is to study the existence and joint continuity of the local times of LMSS, and also the local Hölder condition of the local times in the set variable. Among the main results of this paper, Theorem 2.4 provides a sufﬁcient and necessary condition for the existence of local times of LMSS; Theorem 3.1 shows a sufﬁcient condition for the joint continuity of local times; and Theorem 4.1 proves a sharp local Hölder condition for the local times in the set variable. All these theorems improve signiﬁcantly the existing results for the local times of multifractional Brownian sheets and linear multifractional stable sheets in the literature.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear multifractional stable sheets in the broad sense: Existence and joint continuity of local times\",\"authors\":\"Yujia Ding, Qidi Peng, Yimin Xiao\",\"doi\":\"10.3150/22-bej1479\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) with α ∈ (0 , 2] , to include both linear multifractional Brownian sheets ( α = 2 ) and linear multifractional stable sheets ( α < 2 ). The purpose of the present paper is to study the existence and joint continuity of the local times of LMSS, and also the local Hölder condition of the local times in the set variable. Among the main results of this paper, Theorem 2.4 provides a sufﬁcient and necessary condition for the existence of local times of LMSS; Theorem 3.1 shows a sufﬁcient condition for the joint continuity of local times; and Theorem 4.1 proves a sharp local Hölder condition for the local times in the set variable. All these theorems improve signiﬁcantly the existing results for the local times of multifractional Brownian sheets and linear multifractional stable sheets in the literature.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2021-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3150/22-bej1479\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3150/22-bej1479","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

我们引入了广义线性多重分形稳定片（LMSS）的概念，其中α∈（0，2]）包括线性多重分形布朗片（α=2）和线性多重分形稳定性片（α<2）。本文的目的是研究LMSS局部时间的存在性和联合连续性，以及局部时间在集合变量中的局部Hölder条件。在本文的主要结果中，定理2.4为LMSS的局部时间的存在提供了一个充分必要的条件；定理3.1给出了局部时间联合连续性的一个充分条件；定理4.1证明了集合变量中局部时间的一个尖锐的局部Hölder条件。所有这些定理都显著地改进了文献中关于多分数布朗表和线性多分数稳定表的局部时间的现有结果。

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

Linear multifractional stable sheets in the broad sense: Existence and joint continuity of local times

We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) with α ∈ (0 , 2] , to include both linear multifractional Brownian sheets ( α = 2 ) and linear multifractional stable sheets ( α < 2 ). The purpose of the present paper is to study the existence and joint continuity of the local times of LMSS, and also the local Hölder condition of the local times in the set variable. Among the main results of this paper, Theorem 2.4 provides a sufﬁcient and necessary condition for the existence of local times of LMSS; Theorem 3.1 shows a sufﬁcient condition for the joint continuity of local times; and Theorem 4.1 proves a sharp local Hölder condition for the local times in the set variable. All these theorems improve signiﬁcantly the existing results for the local times of multifractional Brownian sheets and linear multifractional stable sheets in the literature.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.