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

Breuer, Lothar (2013) The resolvent and expected local times for Markov-modulated Brownian motion with phase-dependent termination rates. Journal of Applied Probability, 50 (2). pp. 430-438. ISSN 0021-9002. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31239)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.

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 re?ected at its in?mum.

Keywords: Markov-modulated Brownian motion; local time; resolvent; Markov-additive

process

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Lothar Breuer
Date Deposited: 04 Oct 2012 07:27 UTC
Last Modified: 16 Nov 2021 10:09 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/31239 (The current URI for this page, for reference purposes)
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