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...

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Detalles Bibliográficos
Autores: Pagnini, G., Dahlenburg, M.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1709
Acceso en línea:http://hdl.handle.net/20.500.11824/1709
https://doi.org/10.1098/rspa.2023.0485
Access Level:acceso abierto
Palabra clave:First-passage time
random walks
Wiener–Hopf integral
Sturm–Liouville systems
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spelling Sturm–Liouville systems for the survival probability in first-passage time problemsPagnini, G.Dahlenburg, M.First-passage timerandom walksWiener–Hopf integralSturm–Liouville systemsWe 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.Predoc Severo Ochoa 2018 grant PRE2018-084427202320232023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1709https://doi.org/10.1098/rspa.2023.0485reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2023.0485info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/CEX2021-001142-Sinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2022-2025Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/17092026-06-19T12:47:47Z
dc.title.none.fl_str_mv Sturm–Liouville systems for the survival probability in first-passage time problems
title Sturm–Liouville systems for the survival probability in first-passage time problems
spellingShingle Sturm–Liouville systems for the survival probability in first-passage time problems
Pagnini, G.
First-passage time
random walks
Wiener–Hopf integral
Sturm–Liouville systems
title_short Sturm–Liouville systems for the survival probability in first-passage time problems
title_full Sturm–Liouville systems for the survival probability in first-passage time problems
title_fullStr Sturm–Liouville systems for the survival probability in first-passage time problems
title_full_unstemmed Sturm–Liouville systems for the survival probability in first-passage time problems
title_sort Sturm–Liouville systems for the survival probability in first-passage time problems
dc.creator.none.fl_str_mv Pagnini, G.
Dahlenburg, M.
author Pagnini, G.
author_facet Pagnini, G.
Dahlenburg, M.
author_role author
author2 Dahlenburg, M.
author2_role author
dc.subject.none.fl_str_mv First-passage time
random walks
Wiener–Hopf integral
Sturm–Liouville systems
topic First-passage time
random walks
Wiener–Hopf integral
Sturm–Liouville systems
description 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.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023
2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1709
https://doi.org/10.1098/rspa.2023.0485
url http://hdl.handle.net/20.500.11824/1709
https://doi.org/10.1098/rspa.2023.0485
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2023.0485
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/CEX2021-001142-S
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2022-2025
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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