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Occupation Times for Markov-Modulated Brownian Motion

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  04 February 2016

Lothar Breuer
Lothar Breuer*
Affiliation:
University of Kent
*
∗ Postal address: Institute of Mathematics and Statistics, University of Kent, Canterbury CT2 7NF, UK. Email address: [email protected]
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Abstract

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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.

Keywords

Markov-modulated Brownian motionoccupation timescale functionMarkov additive process

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60G51: Processes with independent increments; L'evy processes 60J55: Local time and additive functionals
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 549 - 565
Copyright
© Applied Probability Trust 

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