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Path decompositions for Markov chains
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 Polya urn.Comment: 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/10.1214/00911790400000023
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