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April, 1977 Conversion of Semimarkov Processes to Chung Processes
Erhan Cinlar
Ann. Probab. 5(2): 180-199 (April, 1977). DOI: 10.1214/aop/1176995844


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.


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Erhan Cinlar. "Conversion of Semimarkov Processes to Chung Processes." Ann. Probab. 5 (2) 180 - 199, April, 1977.


Published: April, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0384.60064
MathSciNet: MR445617
Digital Object Identifier: 10.1214/aop/1176995844

Primary: 60G05
Secondary: 60G17 , 60J25 , 60K15

Keywords: Chung process , random sets , random time changes , Regenerative systems , sample paths , Semimarkov process , strong Markov property

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 2 • April, 1977
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