Journal of Applied Probability

Occupation times for Markov-modulated Brownian motion

Lothar Breuer

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Abstract

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

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

Dates
First available in Project Euclid: 16 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1339878804

Digital Object Identifier
doi:10.1239/jap/1339878804

Mathematical Reviews number (MathSciNet)
MR2977813

Zentralblatt MATH identifier
1258.60046

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

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

Citation

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


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