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

Nicolas Champagnat 1, 2 Denis Villemonais 1, 3, 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
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.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-01188172
Contributor : Nicolas Champagnat <>
Submitted on : Friday, August 28, 2015 - 3:13:13 PM
Last modification on : Tuesday, March 2, 2021 - 5:12:05 PM

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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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