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Journal Articles Probability Theory and Related Fields Year : 2016

Exponential convergence to quasi-stationary distribution and Q-process

Abstract

For general, almost surely absorbed Markov processes, we obtain necessary and sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the $Q$-process (the process conditioned to never be absorbed). We apply these results to one-dimensional birth and death processes with catastrophes, multi-dimensional birth and death processes, infinite-dimensional population models with Brownian mutations and neutron transport dynamics absorbed at the boundary of a bounded domain.
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Dates and versions

hal-00973509 , version 1 (04-04-2014)
hal-00973509 , version 2 (19-12-2014)

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Nicolas Champagnat, Denis Villemonais. Exponential convergence to quasi-stationary distribution and Q-process. Probability Theory and Related Fields, 2016, 164 (1), pp.243-283. ⟨10.1007/s00440-014-0611-7⟩. ⟨hal-00973509v2⟩
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