Exponential convergence to quasi-stationary distribution and $$$$-process |
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Authors: | Nicolas?Champagnat Email author" target="_blank">Denis?VillemonaisEmail author |
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Institution: | 1.Université de Lorraine, IECN,Vand?uvre-lès-Nancy Cedex,France;2.Inria, TOSCA Team,Villers-lès-Nancy,France |
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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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