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Journal Articles Electronic Communications in Probability Year : 2017

Uniform convergence to the Q-process

Abstract

The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribution of the process. Conversely, we prove that, if a conditioned process converges uniformly to a conservative Markov process which is itself ergodic, then it admits a unique quasi-stationary distribution and converges toward it exponentially fast, uniformly in its initial distribution. As an application, we provide a conditional ergodic theorem.
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Dates and versions

hal-01395727 , version 1 (11-11-2016)
hal-01395727 , version 2 (07-04-2017)

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Nicolas Champagnat, Denis Villemonais. Uniform convergence to the Q-process. Electronic Communications in Probability, 2017, 22 (33), pp.1-7. ⟨10.1214/17-ECP63⟩. ⟨hal-01395727v2⟩
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