Uniform convergence to the Q-process

Research paper by Nicolas Champagnat, Denis Villemonais

Indexed on: 08 Nov '16Published on: 08 Nov '16Published in: arXiv - Mathematics - Probability

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.