The First-Passage Area of Wiener Process withStochastic Resetting

IF 1 4区数学 Q3 STATISTICS & PROBABILITY

Methodology and Computing in Applied Probability 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.

Abstract Image

查看原文本刊更多论文

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。

求助全文

约1分钟内获得全文求助全文

来源期刊

Methodology and Computing in Applied Probability 数学-统计学与概率论

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

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