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

• Autorzy: Witold Bednorz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
• 65C05: Monte Carlo methods
• 60K05: Renewal theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2013
• Tom: 40
• Numer: 2
• Strony: 129-165

Daty

wydano

2013

Twórcy

autor

Witold Bednorz

• Institute of Mathematics, Warsaw University, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/am40-2-1