The Kendall theorem and its application to the geometric ergodicity of Markov chains
Tom 40 / 2013
Applicationes Mathematicae 40 (2013), 129-165
MSC: Primary 60J20; Secondary 60K05, 65C05.
DOI: 10.4064/am40-2-1
Streszczenie
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.
