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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todo:paper_00219002_v48_n2_p322_Asselah2023-10-03T14:22:36Z Quasistationary distributions and fleming-viot processes in finite spaces Asselah, A. Ferrari, P.A. Groisman, P. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Asselah, A. Ferrari, P.A. Groisman, P. 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. |
| format |
JOUR |
| author |
Asselah, A. Ferrari, P.A. Groisman, P. |
| author_facet |
Asselah, A. Ferrari, P.A. Groisman, P. |
| author_sort |
Asselah, A. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00219002_v48_n2_p322_Asselah |
| work_keys_str_mv |
AT asselaha quasistationarydistributionsandflemingviotprocessesinfinitespaces AT ferraripa quasistationarydistributionsandflemingviotprocessesinfinitespaces AT groismanp quasistationarydistributionsandflemingviotprocessesinfinitespaces |
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1807316123742371840 |