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2017 Uniform convergence to the $Q$-process
Nicolas Champagnat, Denis Villemonais
Electron. Commun. Probab. 22: 1-7 (2017). DOI: 10.1214/17-ECP63

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.

Citation

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Nicolas Champagnat. Denis Villemonais. "Uniform convergence to the $Q$-process." Electron. Commun. Probab. 22 1 - 7, 2017. https://doi.org/10.1214/17-ECP63

Information

Received: 15 November 2016; Accepted: 23 May 2017; Published: 2017
First available in Project Euclid: 13 June 2017

zbMATH: 1368.60079
MathSciNet: MR3663104
Digital Object Identifier: 10.1214/17-ECP63

Subjects:
Primary: 37A25, 60B10, 60J25

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