The Kendall theorem and its application to the geometric ergodicity of Markov chains

Volume 40 / 2013

Witold Bednorz Applicationes Mathematicae 40 (2013), 129-165 MSC: Primary 60J20; Secondary 60K05, 65C05. DOI: 10.4064/am40-2-1

Abstract

We give an improved quantitative version of the Kendall theorem. The Kendall theorem states that under mild conditions imposed on a probability distribution on the positive integers (i.e. a probability sequence) one can prove convergence of its renewal sequence. Due to the well-known property (the first entrance last exit decomposition) such results are of interest in the stability theory of time-homogeneous Markov chains. In particular this approach may be used to measure rates of convergence of geometrically ergodic Markov chains and consequently implies estimates on convergence of MCMC estimators.

Authors

  • Witold BednorzInstitute of Mathematics
    Warsaw University
    02-097 Warszawa, Poland
    e-mail

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