Simulation of Quasi-stationary distributions on countable spaces

Quasi-stationary distributions QSD have been widely studied since the pioneering work of Kolmogorov (1938), Yaglom (1947) and Sevastyanov (1951). They appear as a natural object when considering Markov processes that are certainly absorbed since they are invariant for the evolution of the distributi...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Groisman, Pablo Jose, Jonckheere, Matthieu Thimothy Samson
Publicado: 2013
Materias:
Fleming-Viot processes
Quasi-stationary distributions
Simulation
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10242953_v19_n3_p521_Groisman
http://hdl.handle.net/20.500.12110/paper_10242953_v19_n3_p521_Groisman
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_10242953_v19_n3_p521_Groisman
record_format dspace
spelling paper:paper_10242953_v19_n3_p521_Groisman2023-06-08T16:00:13Z Simulation of Quasi-stationary distributions on countable spaces Groisman, Pablo Jose Jonckheere, Matthieu Thimothy Samson Fleming-Viot processes Quasi-stationary distributions Simulation Quasi-stationary distributions QSD have been widely studied since the pioneering work of Kolmogorov (1938), Yaglom (1947) and Sevastyanov (1951). They appear as a natural object when considering Markov processes that are certainly absorbed since they are invariant for the evolution of the distribution of the process conditioned on not being absorbed. They hence appropriately describe the state of the process at large times for non absorbed paths. Unlike invariant distributions for Markov processes, QSD are solutions of a non-linear equation and there can be 0, 1 or an infinity of them. Also, they cannot be obtained as Cesàro limits of Markovian dynamics. These facts make the computation of QSDs a nontrivial matter. We review different approximation methods for QSD that are useful for simulation purposes, mainly focused on Fleming-Viot dynamics. We also give some alternative proofs and extensions of known results. © Polymat, Moscow 2013. Fil:Groisman, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Jonckheere, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10242953_v19_n3_p521_Groisman http://hdl.handle.net/20.500.12110/paper_10242953_v19_n3_p521_Groisman
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Fleming-Viot processes
Quasi-stationary distributions
Simulation
spellingShingle Fleming-Viot processes
Quasi-stationary distributions
Simulation
Groisman, Pablo Jose
Jonckheere, Matthieu Thimothy Samson
Simulation of Quasi-stationary distributions on countable spaces
topic_facet Fleming-Viot processes
Quasi-stationary distributions
Simulation
description Quasi-stationary distributions QSD have been widely studied since the pioneering work of Kolmogorov (1938), Yaglom (1947) and Sevastyanov (1951). They appear as a natural object when considering Markov processes that are certainly absorbed since they are invariant for the evolution of the distribution of the process conditioned on not being absorbed. They hence appropriately describe the state of the process at large times for non absorbed paths. Unlike invariant distributions for Markov processes, QSD are solutions of a non-linear equation and there can be 0, 1 or an infinity of them. Also, they cannot be obtained as Cesàro limits of Markovian dynamics. These facts make the computation of QSDs a nontrivial matter. We review different approximation methods for QSD that are useful for simulation purposes, mainly focused on Fleming-Viot dynamics. We also give some alternative proofs and extensions of known results. © Polymat, Moscow 2013.
author Groisman, Pablo Jose
Jonckheere, Matthieu Thimothy Samson
author_facet Groisman, Pablo Jose
Jonckheere, Matthieu Thimothy Samson
author_sort Groisman, Pablo Jose
title Simulation of Quasi-stationary distributions on countable spaces
title_short Simulation of Quasi-stationary distributions on countable spaces
title_full Simulation of Quasi-stationary distributions on countable spaces
title_fullStr Simulation of Quasi-stationary distributions on countable spaces
title_full_unstemmed Simulation of Quasi-stationary distributions on countable spaces
title_sort simulation of quasi-stationary distributions on countable spaces
publishDate 2013
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10242953_v19_n3_p521_Groisman
http://hdl.handle.net/20.500.12110/paper_10242953_v19_n3_p521_Groisman
work_keys_str_mv AT groismanpablojose simulationofquasistationarydistributionsoncountablespaces
AT jonckheerematthieuthimothysamson simulationofquasistationarydistributionsoncountablespaces
_version_ 1768544145211654144

Ejemplares similares