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arXiv · 2311.12240

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

M. Dahlenburg·G. Pagnini
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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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BibTeXRIS

M. Dahlenburg, G. Pagnini. 2023-11-20. Sturm-Liouville systems for the survival probability in first-passage time problems. https://doi.org/10.1098/rspa.2023.0485

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