Sturm–Liouville systems for the survival probability in first-passage time problems

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2023-11-01 DOI:10.1098/rspa.2023.0485
Marcus Dahlenburg, Gianni Pagnini
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引用次数: 1

Abstract

We derive a Sturm–Liouville system of equations for the exact calculation of the survival probability in first-passage time problems. This system is the one associated with the Wiener–Hopf integral equation obtained from the theory of random walks. The derived approach is an alternative to the existing literature and we tested it against direct calculations from both discrete- and continuous-time random walks in a manageable, but meaningful, example. Within this framework, the Sparre Andersen theorem results to be a boundary condition for the system.
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首次通过时间问题中生存概率的Sturm-Liouville系统
我们导出了一个Sturm-Liouville方程组,用于精确计算首次通过时间问题的生存概率。该系统与由随机游走理论得到的Wiener-Hopf积分方程相关联。导出的方法是现有文献的替代方案,我们在一个可管理但有意义的示例中对离散时间和连续时间随机漫步的直接计算进行了测试。在这个框架内,Sparre Andersen定理可以作为系统的边界条件。
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
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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