Path decompositions for Markov chains

2004/04/01 by Götz Kersting, Gotz Kersting, Kaya Memisoglu +1
Computer Science · Mathematics · #Formal Methods in Verification #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #math.PR #msc:60J10 #msc:60J45.

paper · pdf · doi:10.1214/009117904000000234

published as Annals of Probability 2004, Vol. 32, No. 2, 1370-1390 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000234

openalex publication_date 2004/04/01 · arxiv created 2004/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present two path decompositions of Markov chains (with general state space) by means of harmonic functions, which are dual to each other. They can be seen as a generalization of Williams’ decomposition of a Brownian motion with drift. The results may be illustrated by a multitude of examples, but we confine ourselves to different types of random walks and the Pólya urn.

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