Quasi-stationary distribution for multi-dimensional birth and death processes conditioned to survival of all coordinates

Nicolas Champagnat 1, 2 Denis Villemonais 2, 1, 3
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
2 Probabilités et statistiques
IECL - Institut Élie Cartan de Lorraine
Abstract : This article studies the quasi-stationary behaviour of multidimensional birth and death processes, modeling the interaction between several species, absorbed when one of the coordinates hits 0. We study models where the absorption rate is not uniformly bounded, contrary to most of the previous works. To handle this natural situation, we develop original Lyapunov function arguments that might apply in other situations with unbounded killing rates. We obtain the exponential convergence in total variation of the conditional distributions to a unique stationary distribution, uniformly with respect to the initial distribution. Our results cover general birth and death models with stronger intra-specific than inter-specific competition, and cases with neutral competition with explicit conditions on the dimension of the process.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.inria.fr/hal-01188172
Contributeur : Nicolas Champagnat <>
Soumis le : vendredi 28 août 2015 - 15:13:13
Dernière modification le : samedi 27 janvier 2018 - 01:31:17

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  • HAL Id : hal-01188172, version 1
  • ARXIV : 1508.03161

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Nicolas Champagnat, Denis Villemonais. Quasi-stationary distribution for multi-dimensional birth and death processes conditioned to survival of all coordinates. 2015. 〈hal-01188172〉

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