Quantitative results for the Fleming–Viot particle system and quasi-stationary distributions in discrete space - Archive ouverte HAL Access content directly
Journal Articles Stochastic Processes and their Applications Year : 2016

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

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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.

Dates and versions

hal-02636688 , version 1 (27-05-2020)

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Bertrand Cloez, Marie-Noémie Thai. Quantitative results for the Fleming–Viot particle system and quasi-stationary distributions in discrete space. Stochastic Processes and their Applications, 2016, 126 (3), pp.680-702. ⟨10.1016/j.spa.2015.09.016⟩. ⟨hal-02636688⟩
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