Journal of Applied Probability

The resolvent and expected local times for Markov-modulated Brownian motion with phase-dependent termination rates

Lothar Breuer

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Abstract

We consider a Markov-modulated Brownian motion (MMBM) with phase-dependent termination rates, i.e. while in a phase i the process terminates with a constant hazard rate ri ≥ 0. For such a process, we determine the matrix of expected local times (at zero) before termination and hence the resolvent. The results are applied to some recent questions arising in the framework of insurance risk. We further provide expressions for the resolvent and the local times at zero of an MMBM reflected at its infimum.

Article information

Source
J. Appl. Probab., Volume 50, Number 2 (2013), 430-438.

Dates
First available in Project Euclid: 19 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1371648951

Digital Object Identifier
doi:10.1239/jap/1371648951

Mathematical Reviews number (MathSciNet)
MR3102490

Zentralblatt MATH identifier
1270.60078

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 local time resolvent Markov-additive process

Citation

Breuer, Lothar. The resolvent and expected local times for Markov-modulated Brownian motion with phase-dependent termination rates. J. Appl. Probab. 50 (2013), no. 2, 430--438. doi:10.1239/jap/1371648951. https://projecteuclid.org/euclid.jap/1371648951


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