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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| Autores principales: | , |
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2011
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| 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 |
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| Sumario: | 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. |
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