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Article Dans Une Revue The Annals of Applied Probability Année : 2017

Ergodicity of inhomogeneous Markov chains through asymptotic pseudotrajectories

Résumé

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.
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Dates et versions

hal-01401981 , version 1 (24-11-2016)
hal-01401981 , version 2 (08-11-2017)

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Michel Benaïm, Florian Bouguet, Bertrand Cloez. Ergodicity of inhomogeneous Markov chains through asymptotic pseudotrajectories. The Annals of Applied Probability, 2017, 27 (5), pp.3004-3049. ⟨10.1214/17-AAP1275⟩. ⟨hal-01401981v2⟩

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