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

Authors
Asmussen, S Kella, O
Citation
S. Asmussen et O. Kella, A multi-dimensional martingale for Markov additive processes and its applications, ADV APPL P, 32(2), 2000, pp. 376-393
Citations number
23
Categorie Soggetti
Mathematics
Journal title
ADVANCES IN APPLIED PROBABILITY
ISSN journal
00018678 → ACNP
Volume
32
Issue
2
Year of publication
2000
Pages
376 - 393
Database
ISI
SICI code
0001-8678(200006)32:2<376:AMMFMA>2.0.ZU;2-4
Abstract
We establish new multidimensional martingales for Markov additive processes and certain modifications of such processes (e.g., such processes with ref lecting barriers). These results generalize corresponding one-dimensional m artingale results for Levy processes. This martingale is then applied to va rious storage processes, queues and Brownian motion models.