Journal of Applied Probability

Occupation times for Markov-modulated Brownian motion

Lothar Breuer

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In this paper we determine the distributions of occupation times of a Markov-modulated Brownian motion (MMBM) in separate intervals before a first passage time or an exit from an interval. We derive the distributions in terms of their Laplace transforms, and we also distinguish between occupation times in different phases. For MMBMs with strictly positive variation parameters, we further propose scale functions.

Article information

J. Appl. Probab., Volume 49, Number 2 (2012), 549-565.

First available in Project Euclid: 16 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60G51: Processes with independent increments; Lévy processes 60J55: Local time and additive functionals

Markov-modulated Brownian motion occupation time scale function Markov additive process


Breuer, Lothar. Occupation times for Markov-modulated Brownian motion. J. Appl. Probab. 49 (2012), no. 2, 549--565. doi:10.1239/jap/1339878804.

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