Uniform convergence to the Q-process

Nicolas Champagnat; Denis Villemonais

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arXiv · 1611.02473

Uniform convergence to the Q-process

Nicolas Champagnat·Denis Villemonais

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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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Nicolas Champagnat, Denis Villemonais. 2016-11-08. Uniform convergence to the Q-process. https://arxiv.org/abs/1611.02473

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