{"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":18442,"journal":{"name":"Methodology and Computing in Applied Probability","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Methodology and Computing in Applied Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11009-023-10069-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
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：
Methodology and Computing in Applied Probability will publish high quality research and review articles in the areas of applied probability that emphasize methodology and computing. Of special interest are articles in important areas of applications that include detailed case studies. Applied probability is a broad research area that is of interest to many scientists in diverse disciplines including: anthropology, biology, communication theory, economics, epidemiology, finance, linguistics, meteorology, operations research, psychology, quality control, reliability theory, sociology and statistics.
The following alphabetical listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interests:
-Algorithms-
Approximations-
Asymptotic Approximations & Expansions-
Combinatorial & Geometric Probability-
Communication Networks-
Extreme Value Theory-
Finance-
Image Analysis-
Inequalities-
Information Theory-
Mathematical Physics-
Molecular Biology-
Monte Carlo Methods-
Order Statistics-
Queuing Theory-
Reliability Theory-
Stochastic Processes
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