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May 2003 Transient Markov arrival processes
Guy Latouche, Marie-Ange Remiche, Peter Taylor
Ann. Appl. Probab. 13(2): 628-640 (May 2003). DOI: 10.1214/aoap/1050689597

Abstract

We define the family of transient Markov arrival processes (transient MAPs) which combine features of transient (or terminating) renewal processes and of the well-known MAPs: transient MAPs are point processes on the line, controlled by a finite Markov chain, which almost surely comprise a finite number of points. We analyze their basic properties.

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Guy Latouche. Marie-Ange Remiche. Peter Taylor. "Transient Markov arrival processes." Ann. Appl. Probab. 13 (2) 628 - 640, May 2003. https://doi.org/10.1214/aoap/1050689597

Information

Published: May 2003
First available in Project Euclid: 18 April 2003

zbMATH: 1030.60067
MathSciNet: MR1970280
Digital Object Identifier: 10.1214/aoap/1050689597

Subjects:
Primary: 60J22
Secondary: 60K37

Keywords: Markov additive process , Markovian arrival process , quasistationary distribution , terminating process , transient process

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 2 • May 2003
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