Sturm–Liouville systems for the survival probability in first-passage time problems
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 exist...
| Autores: | , |
|---|---|
| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1709 |
| Acesso em linha: | http://hdl.handle.net/20.500.11824/1709 https://doi.org/10.1098/rspa.2023.0485 |
| Access Level: | acceso abierto |
| Palavra-chave: | First-passage time random walks Wiener–Hopf integral Sturm–Liouville systems |
| Resumo: | 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. |
|---|