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.
Publié le : 2004-04-14
Classification:
Markov chain,
path decomposition,
harmonic function,
change of measure,
h-transform,
duality,
random walk,
60J10,
60J45
@article{1084884854,
author = {Kersting, G\"otz and Memi\c so\v glu, Kaya},
title = {Path decompositions for Markov chains},
journal = {Ann. Probab.},
volume = {32},
number = {1A},
year = {2004},
pages = { 1370-1390},
language = {en},
url = {http://dml.mathdoc.fr/item/1084884854}
}
Kersting, Götz; Memişoǧlu, Kaya. Path decompositions for Markov chains. Ann. Probab., Tome 32 (2004) no. 1A, pp. 1370-1390. http://gdmltest.u-ga.fr/item/1084884854/