A Brownian motion with two reflecting barriers and Markov-modulated speed

Autor(en): Kella, O
Stadje, W 
Stichwörter: Brownian motion; double barrier; Markov modulated; Mathematics; multidimensional martingale; reflected Brownian motion; state-dependent speed; Statistics & Probability; two-sided reflection
Erscheinungsdatum: 2004
Herausgeber: CAMBRIDGE UNIV PRESS
Journal: JOURNAL OF APPLIED PROBABILITY
Volumen: 41
Ausgabe: 4
Startseite: 1237
Seitenende: 1242
Zusammenfassung: 
We consider a Brownian motion with time-reversible Markov-modulated speed and two reflecting barriers. A methodology depending on a certain multidimensional martingale together with some linear algebra is applied in order to explicitly compute the stationary distribution of the joint process of the content level and the state of the underlying Markov chain. It is shown that the stationary distribution is such that the two quantities are independent. The long-run average push at the two barriers at each of the states is also computed.
ISSN: 00219002
DOI: 10.1239/jap/1101840571

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