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...

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Autores principales: Groisman, P., Jonckheere, M.
Formato: JOUR
Materias:
Fleming-Viot processes
Quasi-stationary distributions
Simulation
Acceso en línea: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 todo:paper_10242953_v19_n3_p521_Groisman
record_format dspace
spelling todo:paper_10242953_v19_n3_p521_Groisman2023-10-03T15:56:54Z Simulation of Quasi-stationary distributions on countable spaces Groisman, P. Jonckheere, M. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, P.
Jonckheere, M.
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.
format JOUR
author Groisman, P.
Jonckheere, M.
author_facet Groisman, P.
Jonckheere, M.
author_sort Groisman, P.
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
url http://hdl.handle.net/20.500.12110/paper_10242953_v19_n3_p521_Groisman
work_keys_str_mv AT groismanp simulationofquasistationarydistributionsoncountablespaces
AT jonckheerem simulationofquasistationarydistributionsoncountablespaces
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