The Annals of Probability
- Ann. Probab.
- Volume 5, Number 2 (1977), 180-199.
Conversion of Semimarkov Processes to Chung Processes
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.
Ann. Probab., Volume 5, Number 2 (1977), 180-199.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G05: Foundations of stochastic processes
Secondary: 60G17: Sample path properties 60J25: Continuous-time Markov processes on general state spaces 60K15: Markov renewal processes, semi-Markov processes
Cinlar, Erhan. Conversion of Semimarkov Processes to Chung Processes. Ann. Probab. 5 (1977), no. 2, 180--199. doi:10.1214/aop/1176995844. https://projecteuclid.org/euclid.aop/1176995844