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A Multi-Dimensional Martingale for Markov Additive Processes and Its Applications

Søren Asmussen and Offer Kella
Advances in Applied Probability
Vol. 32, No. 2 (Jun., 2000), pp. 376-393
Stable URL: http://www.jstor.org/stable/1428194
Page Count: 18
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A Multi-Dimensional Martingale for Markov Additive Processes and Its Applications
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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.

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