Front propagation and quasi-stationary distributions for one-dimensional Lévy processes

Autores
Groisman, Pablo Jose; Jonckheere, Matthieu Thimothy Samson
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We jointly investigate the existence of quasi-stationary distributions for one dimensional Lévy processes and the existence of traveling waves for the Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation associated with the same motion. Using probabilistic ideas developed by S. Harris, we show that the existence of a traveling wave for the F-KPP equation associated with a centered Lévy processes that branches at rate r and travels at velocity c is equivalent to the existence of a quasi-stationary distribution for a Lévy process with the same movement but drifted by −c and killed at zero, with mean absorption time 1/r. This also extends the known existence conditions in both contexts. As it is discussed in [12], this is not just a coincidence but the consequence of a relation between these two phenomena.
Fil: Groisman, Pablo Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Materia
QUASI-STATIONARY MEASURES
TRAVELLING WAVES
BRANCHING LÉVY PROCESSES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/55507
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Front propagation and quasi-stationary distributions for one-dimensional Lévy processesGroisman, Pablo JoseJonckheere, Matthieu Thimothy SamsonQUASI-STATIONARY MEASURESTRAVELLING WAVESBRANCHING LÉVY PROCESSEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We jointly investigate the existence of quasi-stationary distributions for one dimensional Lévy processes and the existence of traveling waves for the Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation associated with the same motion. Using probabilistic ideas developed by S. Harris, we show that the existence of a traveling wave for the F-KPP equation associated with a centered Lévy processes that branches at rate r and travels at velocity c is equivalent to the existence of a quasi-stationary distribution for a Lévy process with the same movement but drifted by −c and killed at zero, with mean absorption time 1/r. This also extends the known existence conditions in both contexts. As it is discussed in [12], this is not just a coincidence but the consequence of a relation between these two phenomena.Fil: Groisman, Pablo Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaUniv Washington2016-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55507Groisman, Pablo Jose; Jonckheere, Matthieu Thimothy Samson; Front propagation and quasi-stationary distributions for one-dimensional Lévy processes; Univ Washington; Electronic Communications In Probability; 23; 93; 9-2016; 1-102331-8422CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/1609.09338info:eu-repo/semantics/altIdentifier/doi/10.1214/18-ECP199info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.ecp/1544843116info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:39:47Zoai:ri.conicet.gov.ar:11336/55507instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:39:47.985CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Front propagation and quasi-stationary distributions for one-dimensional Lévy processes
title Front propagation and quasi-stationary distributions for one-dimensional Lévy processes
spellingShingle Front propagation and quasi-stationary distributions for one-dimensional Lévy processes
Groisman, Pablo Jose
QUASI-STATIONARY MEASURES
TRAVELLING WAVES
BRANCHING LÉVY PROCESSES
title_short Front propagation and quasi-stationary distributions for one-dimensional Lévy processes
title_full Front propagation and quasi-stationary distributions for one-dimensional Lévy processes
title_fullStr Front propagation and quasi-stationary distributions for one-dimensional Lévy processes
title_full_unstemmed Front propagation and quasi-stationary distributions for one-dimensional Lévy processes
title_sort Front propagation and quasi-stationary distributions for one-dimensional Lévy processes
dc.creator.none.fl_str_mv Groisman, Pablo Jose
Jonckheere, Matthieu Thimothy Samson
author Groisman, Pablo Jose
author_facet Groisman, Pablo Jose
Jonckheere, Matthieu Thimothy Samson
author_role author
author2 Jonckheere, Matthieu Thimothy Samson
author2_role author
dc.subject.none.fl_str_mv QUASI-STATIONARY MEASURES
TRAVELLING WAVES
BRANCHING LÉVY PROCESSES
topic QUASI-STATIONARY MEASURES
TRAVELLING WAVES
BRANCHING LÉVY PROCESSES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We jointly investigate the existence of quasi-stationary distributions for one dimensional Lévy processes and the existence of traveling waves for the Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation associated with the same motion. Using probabilistic ideas developed by S. Harris, we show that the existence of a traveling wave for the F-KPP equation associated with a centered Lévy processes that branches at rate r and travels at velocity c is equivalent to the existence of a quasi-stationary distribution for a Lévy process with the same movement but drifted by −c and killed at zero, with mean absorption time 1/r. This also extends the known existence conditions in both contexts. As it is discussed in [12], this is not just a coincidence but the consequence of a relation between these two phenomena.
Fil: Groisman, Pablo Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
description We jointly investigate the existence of quasi-stationary distributions for one dimensional Lévy processes and the existence of traveling waves for the Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation associated with the same motion. Using probabilistic ideas developed by S. Harris, we show that the existence of a traveling wave for the F-KPP equation associated with a centered Lévy processes that branches at rate r and travels at velocity c is equivalent to the existence of a quasi-stationary distribution for a Lévy process with the same movement but drifted by −c and killed at zero, with mean absorption time 1/r. This also extends the known existence conditions in both contexts. As it is discussed in [12], this is not just a coincidence but the consequence of a relation between these two phenomena.
publishDate 2016
dc.date.none.fl_str_mv 2016-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/55507
Groisman, Pablo Jose; Jonckheere, Matthieu Thimothy Samson; Front propagation and quasi-stationary distributions for one-dimensional Lévy processes; Univ Washington; Electronic Communications In Probability; 23; 93; 9-2016; 1-10
2331-8422
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55507
identifier_str_mv Groisman, Pablo Jose; Jonckheere, Matthieu Thimothy Samson; Front propagation and quasi-stationary distributions for one-dimensional Lévy processes; Univ Washington; Electronic Communications In Probability; 23; 93; 9-2016; 1-10
2331-8422
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/1609.09338
info:eu-repo/semantics/altIdentifier/doi/10.1214/18-ECP199
info:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.ecp/1544843116
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Univ Washington
publisher.none.fl_str_mv Univ Washington
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844613259082072064
score 13.070432

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