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Unique quasi-stationary distribution, with a possibly stabilizing extinction

Abstract : We establish 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 conditionned upon never being absorbed. The technique relies on a coupling procedure that is related to Harris recurrence (for Markov Chains). It applies to general continuous-time and continuous-space Markov processes. The main novelty is that we modulate each coupling step depending both on a final horizon of time (for survival) and on the initial distribution. By this way, we could notably include in the convergence a dependency on the initial condition. As an illustration, we consider a continuous-time birth-death process with catastrophes and a diffusion process describing a (localized) population adapting to its environment.
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https://hal-univ-eiffel.archives-ouvertes.fr/hal-03781505
Contributor : Aurélien Velleret Connect in order to contact the contributor
Submitted on : Tuesday, September 20, 2022 - 1:59:42 PM
Last modification on : Wednesday, September 28, 2022 - 5:45:07 AM

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Aurélien Velleret. Unique quasi-stationary distribution, with a possibly stabilizing extinction. Stochastic Processes and their Applications, 2022, 148, pp.98-138. ⟨10.1016/j.spa.2022.02.004⟩. ⟨hal-03781505⟩

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