{"title":"随机重置的Wiener过程的第一通道区","authors":"Mario Abundo","doi":"10.1007/s11009-023-10069-4","DOIUrl":null,"url":null,"abstract":"<p>For a one-dimensional Wiener process with stochastic resetting <span>\\(\\mathcal{X}(t)\\)</span>, obtained from an underlying Wiener process <i>X</i>(<i>t</i>), we study the statistical properties of its first-passage time through zero, when starting from <span>\\(X>0,\\)</span> and its first-passage area, that is the random area enclosed between the time axis and the path of the process <span>\\(\\mathcal{X} (t)\\)</span> up to the first-passage time through zero. By making use of solutions of certain associated ODEs, we are able to find explicit expressions for the Laplace transforms of the first-passage time and the first-passage area, and their single and joint moments.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The First-Passage Area of Wiener Process withStochastic Resetting\",\"authors\":\"Mario Abundo\",\"doi\":\"10.1007/s11009-023-10069-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For a one-dimensional Wiener process with stochastic resetting <span>\\\\(\\\\mathcal{X}(t)\\\\)</span>, obtained from an underlying Wiener process <i>X</i>(<i>t</i>), we study the statistical properties of its first-passage time through zero, when starting from <span>\\\\(X>0,\\\\)</span> and its first-passage area, that is the random area enclosed between the time axis and the path of the process <span>\\\\(\\\\mathcal{X} (t)\\\\)</span> up to the first-passage time through zero. By making use of solutions of certain associated ODEs, we are able to find explicit expressions for the Laplace transforms of the first-passage time and the first-passage area, and their single and joint moments.</p>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-11-29\",\"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/10.1007/s11009-023-10069-4\",\"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/10.1007/s11009-023-10069-4","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
The First-Passage Area of Wiener Process withStochastic Resetting
For a one-dimensional Wiener process with stochastic resetting \(\mathcal{X}(t)\), obtained from an underlying Wiener process X(t), we study the statistical properties of its first-passage time through zero, when starting from \(X>0,\) and its first-passage area, that is the random area enclosed between the time axis and the path of the process \(\mathcal{X} (t)\) up to the first-passage time through zero. By making use of solutions of certain associated ODEs, we are able to find explicit expressions for the Laplace transforms of the first-passage time and the first-passage area, and their single and joint moments.
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.