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A multi-dimensional martingale for Markov additive processes and its applications

Part of: Special processes

Published online by Cambridge University Press:  01 July 2016

Søren Asmussen  and
Offer Kella
Søren Asmussen*
Affiliation:
University of Lund
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
*
∗ Postal address: Department of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden. Email address: asmus@maths.lth.se
∗∗ Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel. Email address: mskella@mscc.huji.ac.il
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Abstract

We establish new multidimensional martingales for Markov additive processes and certain modifications of such processes (e.g., such processes with reflecting barriers). These results generalize corresponding one-dimensional martingale results for Lévy processes. This martingale is then applied to various storage processes, queues and Brownian motion models.

Keywords

Lévy processEOQ modelfluid queuesMarkov modulationmultivariate martingalereflected Brownian motionstorage process

MSC classification

Primary: 60K25: Queueing theory

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 2 , June 2000 , pp. 376 - 393
Copyright
Copyright © Applied Probability Trust 2000 

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Footnotes

Supported in part by grant 794/97 from the Israel Science Foundation.

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