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Potential Measures of One-Sided Markov Additive Processes with Reflecting and Terminating Barriers

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  30 January 2018

Jevgenijs Ivanovs
Jevgenijs Ivanovs*
Affiliation:
University of Lausanne
*
∗ Postal address: Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Quartier UNIL-Dorigny, 1015 Lausanne, Switzerland. Email address: jevgenijs.ivanovs@unil.ch
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Abstract

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Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and nondefective processes, and all possible scenarios, we identify the corresponding potential measures, which help to generalize a number of results for one-sided Lévy processes. The resulting rather neat formulae have various applications in risk and queueing theories, and, in particular, they lead to quasistationary distributions of the corresponding processes.

Keywords

Markov modulationexit from an intervalresolventtime reversaltransient analysisquasistationaryquasistationary distribution

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 51 , Issue 4 , December 2014 , pp. 1154 - 1170
Copyright
© Applied Probability Trust 

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