Coefficients of ergodicity are an important tool in measuring convergence of Markov chains. We explore possibilities to generalise the concept to imprecise Markov chains. We find that this can be done in at least two different ways, which both have interesting implications in the study of convergence of imprecise Markov chains. Thus we extend the existing definition of the uniform coefficient of ergodicity and define a new so-called weak coefficient of ergodicity. The definition is based on the endowment of a structure of a metric space to the class of imprecise probabilities. We show that this is possible to do in some different ways, which turn out to coincide.
Keywords. Markov chain, imprecise Markov chain, coefficient of ergodicity, lower expectation, upper expectation
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Faculty of Social Sciences
University of Ljubljana
Kardeljeva ploščad 5
Department of Mathematics
University of Bayreuth