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2020 $V$-geometrical ergodicity of Markov kernels via finite-rank approximations
Loïc Hervé, James Ledoux
Electron. Commun. Probab. 25: 1-12 (2020). DOI: 10.1214/20-ECP303


Under the standard drift/minorization and strong aperiodicity assumptions, this paper provides an original and quite direct approach of the $V$-geometrical ergodicity of a general Markov kernel $P$, which is by now a classical framework in Markov modelling. This is based on an explicit approximation of the iterates of $P$ by positive finite-rank operators, combined with the Krein-Rutman theorem in its version on topological dual spaces. Moreover this allows us to get a new bound on the spectral gap of the transition kernel. This new approach is expected to shed new light on the role and on the interest of the above mentioned drift/minorization and strong aperiodicity assumptions in $V$-geometrical ergodicity.


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Loïc Hervé. James Ledoux. "$V$-geometrical ergodicity of Markov kernels via finite-rank approximations." Electron. Commun. Probab. 25 1 - 12, 2020.


Received: 13 December 2019; Accepted: 28 February 2020; Published: 2020
First available in Project Euclid: 14 March 2020

zbMATH: 1434.60175
MathSciNet: MR4089730
Digital Object Identifier: 10.1214/20-ECP303

Primary: 60J05

Keywords: drift condition , geometric ergodicity , minorization condition , rate of convergence , spectral gap


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