The Annals of Probability

On the Structure of Semimarkov Processes Compared with Chung Processes

Erhan Cinlar

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Abstract

Semimarkov processes with discrete state spaces are considered without restrictions on their probability laws. They admit states where every visit lasts a positive time even though there may be infinitely many such visits in a finite interval. These are called unstable holding states as opposed to the stable holding states which are encountered in Markov processes. Further, it is possible to have instantaneous states at which the behavior is that at an ordinary instantaneous state of a Chung process, or that at a sticky boundary point, or that at a nonsticky point. To convert such processes to Chung processes, each unstable state is split into infinitely many stable ones, and then a random time change is effected whereby some sets of constancy are dilated, and sojourn intervals are altered to have exponentially distributed lengths.

Article information

Source
Ann. Probab., Volume 4, Number 3 (1976), 402-417.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996089

Digital Object Identifier
doi:10.1214/aop/1176996089

Mathematical Reviews number (MathSciNet)
MR402934

Zentralblatt MATH identifier
0375.60099

JSTOR
links.jstor.org

Subjects
Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60G17: Sample path properties 60J25: Continuous-time Markov processes on general state spaces

Keywords
Semimarkov processes Markov processes classification of states sample path behavior time changes

Citation

Cinlar, Erhan. On the Structure of Semimarkov Processes Compared with Chung Processes. Ann. Probab. 4 (1976), no. 3, 402--417. doi:10.1214/aop/1176996089. https://projecteuclid.org/euclid.aop/1176996089


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