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Ergodicity of inhomogeneous Markov chains through asymptotic pseudotrajectories. (English) Zbl 1379.60077

Summary: 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.

MSC:

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