Advances in Applied Probability

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

Søren Asmussen and Offer Kella

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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.

Article information

Adv. in Appl. Probab. Volume 32, Number 2 (2000), 376-393.

First available in Project Euclid: 12 February 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J30 60K25: Queueing theory [See also 68M20, 90B22]

Lévy process EOQ model fluid queues Markov modulation multivariate martingale reflected Brownian motion storage process


Asmussen, Søren; Kella, Offer. A multi-dimensional martingale for Markov additive processes and its applications. Adv. in Appl. Probab. 32 (2000), no. 2, 376--393. doi:10.1239/aap/1013540169.

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