Given a Markov chain with stationary transition probabilities, we study random times $\tau$ determined by the evolution of the Markov chain for which either the pre-$\tau$ or post-$\tau$ process is Markovian with stationary transition probabilities. A complete description is given of all such random times which admit a conditional independence property analogous to the strong Markov property at a stopping time.
Publié le : 1977-06-14
Classification:
Markov chain,
path decomposition,
birth time,
death time,
conditional independence of path fragments,
60J10,
60G40
@article{1176995803,
author = {Jacobsen, M. and Pitman, J. W.},
title = {Birth, Death and Conditioning of Markov Chains},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 430-450},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995803}
}
Jacobsen, M.; Pitman, J. W. Birth, Death and Conditioning of Markov Chains. Ann. Probab., Tome 5 (1977) no. 6, pp. 430-450. http://gdmltest.u-ga.fr/item/1176995803/