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...

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Bibliographic Details
Published in:The Annals of probability 2004-04, Vol.32 (2), p.1370-1390
Main Authors: Kersting, Götz, Memişoǧlu, Kaya
Format: Article
Language:English
Subjects:
60J10
60J45
Brownian motion
change of measure
Decomposition
duality
Exact sciences and technology
h-transform
harmonic function
Harmonic functions
Markov analysis
Markov chain
Markov chains
Markov processes
Martingales
Mathematical analysis
Mathematics
path decomposition
Probabilities
Probability and statistics
Probability theory and stochastic processes
Random variables
Random walk
Sciences and techniques of general use
Stopping distances
Studies
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Description
Summary: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.
ISSN:0091-1798
2168-894X
DOI:10.1214/009117904000000234