Quasi-stationary distributions and Fleming-Viot processes in finite spaces

Autores
Asselah, Amine; Ferrari, Pablo Augusto; Groisman, Pablo Jose
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Consider a continuous-time Markov process with transition rates matrix Q in the state space Λ ⋃ {0}. In the associated Fleming-Viot process N particles evolve independently in Λ with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Λ is finite, we show that the empirical distribution of the particles at a fixed time converges as N → ∞ to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N → ∞ to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1 / N.
Fil: Asselah, Amine. Universite de Paris; Francia
Fil: Ferrari, Pablo Augusto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidade de Sao Paulo; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Groisman, Pablo Jose. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Fleming Viot Processes
Quasi stationary distributions
Markov 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:11336/14929
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Quasi-stationary distributions and Fleming-Viot processes in finite spacesAsselah, AmineFerrari, Pablo AugustoGroisman, Pablo JoseFleming Viot ProcessesQuasi stationary distributionsMarkov processeshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Consider a continuous-time Markov process with transition rates matrix Q in the state space Λ ⋃ {0}. In the associated Fleming-Viot process N particles evolve independently in Λ with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Λ is finite, we show that the empirical distribution of the particles at a fixed time converges as N → ∞ to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N → ∞ to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1 / N.Fil: Asselah, Amine. Universite de Paris; FranciaFil: Ferrari, Pablo Augusto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidade de Sao Paulo; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Groisman, Pablo Jose. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaApplied Probability Trust2011-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14929Asselah, Amine; Ferrari, Pablo Augusto; Groisman, Pablo Jose; Quasi-stationary distributions and Fleming-Viot processes in finite spaces; Applied Probability Trust; Journal Of Applied Probability; 48; 2; 6-2011; 322-3320021-9002enginfo:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/journal-of-applied-probability/article/quasistationary-distributions-and-flemingviot-processes-in-finite-spaces/5B4539097B46FACC95040F4D2A23CA7B#info:eu-repo/semantics/altIdentifier/doi/10.1017/S0021900200007907info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:58:42Zoai:ri.conicet.gov.ar:11336/14929instacron: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 09:58:42.811CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quasi-stationary distributions and Fleming-Viot processes in finite spaces
title Quasi-stationary distributions and Fleming-Viot processes in finite spaces
spellingShingle Quasi-stationary distributions and Fleming-Viot processes in finite spaces
Asselah, Amine
Fleming Viot Processes
Quasi stationary distributions
Markov processes
title_short Quasi-stationary distributions and Fleming-Viot processes in finite spaces
title_full Quasi-stationary distributions and Fleming-Viot processes in finite spaces
title_fullStr Quasi-stationary distributions and Fleming-Viot processes in finite spaces
title_full_unstemmed Quasi-stationary distributions and Fleming-Viot processes in finite spaces
title_sort Quasi-stationary distributions and Fleming-Viot processes in finite spaces
dc.creator.none.fl_str_mv Asselah, Amine
Ferrari, Pablo Augusto
Groisman, Pablo Jose
author Asselah, Amine
author_facet Asselah, Amine
Ferrari, Pablo Augusto
Groisman, Pablo Jose
author_role author
author2 Ferrari, Pablo Augusto
Groisman, Pablo Jose
author2_role author
author
dc.subject.none.fl_str_mv Fleming Viot Processes
Quasi stationary distributions
Markov processes
topic Fleming Viot Processes
Quasi stationary distributions
Markov 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 Consider a continuous-time Markov process with transition rates matrix Q in the state space Λ ⋃ {0}. In the associated Fleming-Viot process N particles evolve independently in Λ with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Λ is finite, we show that the empirical distribution of the particles at a fixed time converges as N → ∞ to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N → ∞ to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1 / N.
Fil: Asselah, Amine. Universite de Paris; Francia
Fil: Ferrari, Pablo Augusto. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidade de Sao Paulo; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Groisman, Pablo Jose. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description Consider a continuous-time Markov process with transition rates matrix Q in the state space Λ ⋃ {0}. In the associated Fleming-Viot process N particles evolve independently in Λ with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Λ is finite, we show that the empirical distribution of the particles at a fixed time converges as N → ∞ to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N → ∞ to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1 / N.
publishDate 2011
dc.date.none.fl_str_mv 2011-06
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/11336/14929
Asselah, Amine; Ferrari, Pablo Augusto; Groisman, Pablo Jose; Quasi-stationary distributions and Fleming-Viot processes in finite spaces; Applied Probability Trust; Journal Of Applied Probability; 48; 2; 6-2011; 322-332
0021-9002
url http://hdl.handle.net/11336/14929
identifier_str_mv Asselah, Amine; Ferrari, Pablo Augusto; Groisman, Pablo Jose; Quasi-stationary distributions and Fleming-Viot processes in finite spaces; Applied Probability Trust; Journal Of Applied Probability; 48; 2; 6-2011; 322-332
0021-9002
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/journal-of-applied-probability/article/quasistationary-distributions-and-flemingviot-processes-in-finite-spaces/5B4539097B46FACC95040F4D2A23CA7B#
info:eu-repo/semantics/altIdentifier/doi/10.1017/S0021900200007907
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
application/pdf
dc.publisher.none.fl_str_mv Applied Probability Trust
publisher.none.fl_str_mv Applied Probability Trust
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
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score 13.070432

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