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On some waiting time problems

Part of: Distribution theory - Probability Stochastic processes Distribution theory Special processes

Published online by Cambridge University Press:  14 July 2016

Valeri T. Stefanov
Valeri T. Stefanov*
Affiliation:
The University of Western Australia
*
∗Postal address: Department of Mathematics and Statistics, The University of Western Australia, Nedlands, WA 6907, Australia. Email address: [email protected]
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Abstract

A unifying technology is introduced for finding explicit closed form expressions for joint moment generating functions of various random quantities associated with some waiting time problems. Sooner and later waiting times are covered for general discrete- and continuous-time models. The models are either Markov chains or semi-Markov processes with a finite number of states. Waiting times associated with generalized phase-type distributions, that are of interest in survival analysis and other areas, are also covered.

Keywords

Markov chainMarkov renewal processstopping timerunexponential familygeneralized phase-type distribution

MSC classification

Primary: 60E10: Characteristic functions; other transforms 60G40: Stopping times; optimal stopping problems; gambling theory 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Secondary: 62E15: Exact distribution theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 756 - 764
Copyright
Copyright © Applied Probability Trust 2000 

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