On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity

Autores
Jonckheere, Matthieu Thimothy Samson; Saglietti, Santiago
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We give necessary and sufficient conditions for laws of large numbers to hold in L2 for the empirical measure of a large class of branching Markov processes, including λ-positive systems but also some λ-transient ones, such as the branching Brownian motion with drift and absorption at 0. This is a significant improvement over previous results on this matter, which had only dealt so far with λ-positive systems. Our approach is purely probabilistic and is based on spinal decompositions and many-to-few lemmas. In addition, we characterize when the limit in question is always strictly positive on the event of survival, and use this characterization to derive a simple method for simulating (quasi-)stationary distributions.
Fil: Jonckheere, Matthieu Thimothy Samson. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Fil: Saglietti, Santiago. Technion - Israel Institute of Technology; Israel
Materia
BRANCHING MARKOV PROCESSES
H-TRANSFORM
LAW OF LARGE NUMBERS
SPINE DECOMPOSITION
Λ-POSITIVITY
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:11336/147402
Acceder
id CONICETDig_d693e986c3f9e1b0ebb45551ea1fb577
oai_identifier_str oai:ri.conicet.gov.ar:11336/147402
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivityJonckheere, Matthieu Thimothy SamsonSaglietti, SantiagoBRANCHING MARKOV PROCESSESH-TRANSFORMLAW OF LARGE NUMBERSSPINE DECOMPOSITIONΛ-POSITIVITYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We give necessary and sufficient conditions for laws of large numbers to hold in L2 for the empirical measure of a large class of branching Markov processes, including λ-positive systems but also some λ-transient ones, such as the branching Brownian motion with drift and absorption at 0. This is a significant improvement over previous results on this matter, which had only dealt so far with λ-positive systems. Our approach is purely probabilistic and is based on spinal decompositions and many-to-few lemmas. In addition, we characterize when the limit in question is always strictly positive on the event of survival, and use this characterization to derive a simple method for simulating (quasi-)stationary distributions.Fil: Jonckheere, Matthieu Thimothy Samson. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaFil: Saglietti, Santiago. Technion - Israel Institute of Technology; IsraelInstitute of Mathematical Statistics2019-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/147402Jonckheere, Matthieu Thimothy Samson; Saglietti, Santiago; On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity; Institute of Mathematical Statistics; Annales de L'institut Henri Poincare-probabilites Et Statistiques; 56; 1; 2-2019; 265-2950246-0203CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.aihp/1580720489#abstractinfo:eu-repo/semantics/altIdentifier/doi/10.1214/19-AIHP961info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-02-26T10:29:35Zoai:ri.conicet.gov.ar:11336/147402instacron: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:34982026-02-26 10:29:36.078CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity
title On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity
spellingShingle On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity
Jonckheere, Matthieu Thimothy Samson
BRANCHING MARKOV PROCESSES
H-TRANSFORM
LAW OF LARGE NUMBERS
SPINE DECOMPOSITION
Λ-POSITIVITY
title_short On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity
title_full On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity
title_fullStr On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity
title_full_unstemmed On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity
title_sort On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity
dc.creator.none.fl_str_mv Jonckheere, Matthieu Thimothy Samson
Saglietti, Santiago
author Jonckheere, Matthieu Thimothy Samson
author_facet Jonckheere, Matthieu Thimothy Samson
Saglietti, Santiago
author_role author
author2 Saglietti, Santiago
author2_role author
dc.subject.none.fl_str_mv BRANCHING MARKOV PROCESSES
H-TRANSFORM
LAW OF LARGE NUMBERS
SPINE DECOMPOSITION
Λ-POSITIVITY
topic BRANCHING MARKOV PROCESSES
H-TRANSFORM
LAW OF LARGE NUMBERS
SPINE DECOMPOSITION
Λ-POSITIVITY
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 give necessary and sufficient conditions for laws of large numbers to hold in L2 for the empirical measure of a large class of branching Markov processes, including λ-positive systems but also some λ-transient ones, such as the branching Brownian motion with drift and absorption at 0. This is a significant improvement over previous results on this matter, which had only dealt so far with λ-positive systems. Our approach is purely probabilistic and is based on spinal decompositions and many-to-few lemmas. In addition, we characterize when the limit in question is always strictly positive on the event of survival, and use this characterization to derive a simple method for simulating (quasi-)stationary distributions.
Fil: Jonckheere, Matthieu Thimothy Samson. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Fil: Saglietti, Santiago. Technion - Israel Institute of Technology; Israel
description We give necessary and sufficient conditions for laws of large numbers to hold in L2 for the empirical measure of a large class of branching Markov processes, including λ-positive systems but also some λ-transient ones, such as the branching Brownian motion with drift and absorption at 0. This is a significant improvement over previous results on this matter, which had only dealt so far with λ-positive systems. Our approach is purely probabilistic and is based on spinal decompositions and many-to-few lemmas. In addition, we characterize when the limit in question is always strictly positive on the event of survival, and use this characterization to derive a simple method for simulating (quasi-)stationary distributions.
publishDate 2019
dc.date.none.fl_str_mv 2019-02
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/11336/147402
Jonckheere, Matthieu Thimothy Samson; Saglietti, Santiago; On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity; Institute of Mathematical Statistics; Annales de L'institut Henri Poincare-probabilites Et Statistiques; 56; 1; 2-2019; 265-295
0246-0203
CONICET Digital
CONICET
url http://hdl.handle.net/11336/147402
identifier_str_mv Jonckheere, Matthieu Thimothy Samson; Saglietti, Santiago; On laws of large numbers in L2 for supercritical branching Markov processes beyond λ-positivity; Institute of Mathematical Statistics; Annales de L'institut Henri Poincare-probabilites Et Statistiques; 56; 1; 2-2019; 265-295
0246-0203
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://projecteuclid.org/euclid.aihp/1580720489#abstract
info:eu-repo/semantics/altIdentifier/doi/10.1214/19-AIHP961
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 Institute of Mathematical Statistics
publisher.none.fl_str_mv Institute of Mathematical Statistics
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_ 1858305996694224896
score 12.665996

Publicaciones similares