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

Published online by Cambridge University Press:  01 July 2016

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

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.

MSC classification

Type
General Applied Probability
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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