Quasistationary distributions and fleming-viot processes in finite spaces

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...

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Detalles Bibliográficos
Autores principales: Ferrari, Pablo Augusto, Groisman, Pablo Jose
Publicado: 2011
Materias:
Fleming-Viot process
Quasistationary distribution
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219002_v48_n2_p322_Asselah
http://hdl.handle.net/20.500.12110/paper_00219002_v48_n2_p322_Asselah
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00219002_v48_n2_p322_Asselah
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spelling paper:paper_00219002_v48_n2_p322_Asselah2023-06-08T14:43:03Z Quasistationary distributions and fleming-viot processes in finite spaces Ferrari, Pablo Augusto Groisman, Pablo Jose Fleming-Viot process Quasistationary distribution 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. © Applied Probability Trust 2011. Fil:Ferrari, P.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Groisman, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219002_v48_n2_p322_Asselah http://hdl.handle.net/20.500.12110/paper_00219002_v48_n2_p322_Asselah
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 process
Quasistationary distribution
spellingShingle Fleming-Viot process
Quasistationary distribution
Ferrari, Pablo Augusto
Groisman, Pablo Jose
Quasistationary distributions and fleming-viot processes in finite spaces
topic_facet Fleming-Viot process
Quasistationary distribution
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. © Applied Probability Trust 2011.
author Ferrari, Pablo Augusto
Groisman, Pablo Jose
author_facet Ferrari, Pablo Augusto
Groisman, Pablo Jose
author_sort Ferrari, Pablo Augusto
title Quasistationary distributions and fleming-viot processes in finite spaces
title_short Quasistationary distributions and fleming-viot processes in finite spaces
title_full Quasistationary distributions and fleming-viot processes in finite spaces
title_fullStr Quasistationary distributions and fleming-viot processes in finite spaces
title_full_unstemmed Quasistationary distributions and fleming-viot processes in finite spaces
title_sort quasistationary distributions and fleming-viot processes in finite spaces
publishDate 2011
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219002_v48_n2_p322_Asselah
http://hdl.handle.net/20.500.12110/paper_00219002_v48_n2_p322_Asselah
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AT groismanpablojose quasistationarydistributionsandflemingviotprocessesinfinitespaces
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