The Annals of Applied Probability

Ergodicity of inhomogeneous Markov chains through asymptotic pseudotrajectories

Michel Benaïm, Florian Bouguet, and Bertrand Cloez

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Abstract

In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a homogeneous (continuous time) Markov process. Renowned examples such as a bandit algorithms, weighted random walks or decreasing step Euler schemes are included in our framework. Our results are related to functional limit theorems, but the approach differs from the standard “Tightness/Identification” argument; our method is unified and based on the notion of pseudotrajectories on the space of probability measures.

Article information

Source
Ann. Appl. Probab., Volume 27, Number 5 (2017), 3004-3049.

Dates
Received: February 2016
Revised: September 2016
First available in Project Euclid: 3 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1509696040

Digital Object Identifier
doi:10.1214/17-AAP1275

Mathematical Reviews number (MathSciNet)
MR3719952

Zentralblatt MATH identifier
1379.60077

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60B10: Convergence of probability measures

Keywords
Markov chain Markov process asymptotic pseudotrajectory quantitative ergodicity random walk bandit algorithm decreasing step Euler scheme

Citation

Benaïm, Michel; Bouguet, Florian; Cloez, Bertrand. Ergodicity of inhomogeneous Markov chains through asymptotic pseudotrajectories. Ann. Appl. Probab. 27 (2017), no. 5, 3004--3049. doi:10.1214/17-AAP1275. https://projecteuclid.org/euclid.aoap/1509696040


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