Uniform convergence to the Q-process
Probability
2017-04-10 v2
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.
Cite
@article{arxiv.1611.02473,
title = {Uniform convergence to the Q-process},
author = {Nicolas Champagnat and Denis Villemonais},
journal= {arXiv preprint arXiv:1611.02473},
year = {2017}
}