Structure of semimarkov processes in the sense of Cinlar (1975) will be clarified by relating them to Chung processes. Start with a semimarkov process. For each attractive instantaneous state whose occupation time is zero, dilate its constancy set so that the occupation time becomes positive; this is achieved by a random time change. Then, mark each sojourn interval of an unstable holding state $i$ by $(i, k)$ if its length is between $1/k$ and $1/(k - 1)$; this is "splitting" the unstable state $i$ to infinitely many stable states $(i, k)$. Finally, replace each sojourn interval (of the original stable states $i$ plus the new stable states $(i, k)$) by an interval of exponentially distributed length. The result is a Chung process modulo some standardization and modification.
Publié le : 1977-04-14
Classification:
Semimarkov process,
Chung process,
strong Markov property,
random time changes,
regenerative systems,
sample paths,
random sets,
60G05,
60G17,
60J25,
60K15
@article{1176995844,
author = {Cinlar, Erhan},
title = {Conversion of Semimarkov Processes to Chung Processes},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 180-199},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995844}
}
Cinlar, Erhan. Conversion of Semimarkov Processes to Chung Processes. Ann. Probab., Tome 5 (1977) no. 6, pp. 180-199. http://gdmltest.u-ga.fr/item/1176995844/