The First-Passage Area of Wiener Process withStochastic Resetting

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-29 DOI:10.1007/s11009-023-10069-4

Mario Abundo

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.

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随机重置的Wiener过程的第一通道区

对于由底层维纳过程X(t)得到的具有随机重置\(\mathcal{X}(t)\)的一维维纳过程，我们研究了其从\(X>0,\)开始的第一次通过零的时间的统计性质，以及它的第一次通过区域，即在时间轴和过程路径\(\mathcal{X} (t)\)之间的随机区域，直到第一次通过零的时间。利用某些关联ode的解，我们可以求出第一遍时间和第一遍面积的拉普拉斯变换及其单弯矩和联合弯矩的显式表达式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.