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June 2011 Quasistationary distributions and Fleming-Viot processes in finite spaces
Amine Asselah, Pablo A. Ferrari, Pablo Groisman
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J. Appl. Probab. 48(2): 322-332 (June 2011). DOI: 10.1239/jap/1308662630


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.


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Amine Asselah. Pablo A. Ferrari. Pablo Groisman. "Quasistationary distributions and Fleming-Viot processes in finite spaces." J. Appl. Probab. 48 (2) 322 - 332, June 2011.


Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1219.60081
MathSciNet: MR2840302
Digital Object Identifier: 10.1239/jap/1308662630

Primary: 60K35
Secondary: 60J25

Keywords: Fleming-Viot process , quasistationary distribution

Rights: Copyright © 2011 Applied Probability Trust


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Vol.48 • No. 2 • June 2011
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