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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Cloez, Bertrand^1,2  Thai, Marie-Noemie³ 

[1] UMR INRA SupAgro MISTEA, Montpellier, France

[2] EPI INRA INRIA MODEMIC, Sophia Antipolis, France

[3] Univ Paris Est Marne La Vallee, Lab Anal & Math Appl, CNRS UMR8050, Marne La Vallee, France

关键词: Fleming-Viot process;    quasi-stationary distributions;    Coupling;    Wasserstein distance;    Chaos propagation;    Commutation relation;   

DOI  :  10.1016/j.spa.2015.09.016

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free