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Quantitative results for the Fleming–Viot particle system and quasi-stationary distributions in discrete space

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  • Cloez, Bertrand
  • Thai, Marie-Noémie

Abstract

We show, for a class of discrete Fleming–Viot (or Moran) type particle systems, that the convergence to the equilibrium is exponential for a suitable Wasserstein coupling distance. The approach provides an explicit quantitative estimate on the rate of convergence. As a consequence, we show that the conditioned process converges exponentially fast to a unique quasi-stationary distribution. Moreover, by estimating the two-particle correlations, we prove that the Fleming–Viot process converges, uniformly in time, to the conditioned process with an explicit rate of convergence. We illustrate our results on the examples of the complete graph and of N particles jumping on two points.

Suggested Citation

  • Cloez, Bertrand & Thai, Marie-Noémie, 2016. "Quantitative results for the Fleming–Viot particle system and quasi-stationary distributions in discrete space," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 680-702.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:3:p:680-702
    DOI: 10.1016/j.spa.2015.09.016
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    References listed on IDEAS

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    1. Moral, P. Del & Miclo, L., 2000. "A Moran particle system approximation of Feynman-Kac formulae," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 193-216, April.
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    Cited by:

    1. Corujo, Josué, 2021. "Dynamics of a Fleming–Viot type particle system on the cycle graph," Stochastic Processes and their Applications, Elsevier, vol. 136(C), pages 57-91.
    2. Cloez, Bertrand & Corujo, Josué, 2022. "Uniform in time propagation of chaos for a Moran model," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 251-285.
    3. Denis Villemonais, 2020. "Lower Bound for the Coarse Ricci Curvature of Continuous-Time Pure-Jump Processes," Journal of Theoretical Probability, Springer, vol. 33(2), pages 954-991, June.

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