Journal of Applied Probability

Quasistationary distributions and Fleming-Viot processes in finite spaces

Amine Asselah, Pablo A. Ferrari, and Pablo Groisman

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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.

Article information

J. Appl. Probab., Volume 48, Number 2 (2011), 322-332.

First available in Project Euclid: 21 June 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J25: Continuous-time Markov processes on general state spaces

Quasistationary distribution Fleming-Viot process


Asselah, Amine; Ferrari, Pablo A.; Groisman, Pablo. Quasistationary distributions and Fleming-Viot processes in finite spaces. J. Appl. Probab. 48 (2011), no. 2, 322--332. doi:10.1239/jap/1308662630.

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