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Quantitative results for the Fleming-Viot particle system in discrete space
Bertrand Cloez,Marie-Noémie Thai +1 more
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For a class of discrete Fleming-Viot (or Moran) type particle systems, the authors showed that the convergence to the equilibrium is exponential for a suitable Wassertein coupling distance.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 Wassertein 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.read more
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Exponential convergence to quasi-stationary distribution and Q-process
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On quantitative convergence to quasi-stationarity
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TL;DR: In this article, the authors considered the long time behavior of absorbing, finite, irreducible Markov processes and showed that only the knowledge of the ratio of the values of the underlying first Dirichlet eigenvector is necessary to come back to the well-investigated situation of the convergence to equilibrium of ergodic finite Markov process.
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A stochastic approximation approach to quasi-stationary distributions on finite spaces
Michel Benaïm,Bertrand Cloez +1 more
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Minimal quasi-stationary distribution approximation for a birth and death process
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