First passage times for Markov additive processes with positive jumps of phase-type

Breuer, Lothar (2008) First passage times for Markov additive processes with positive jumps of phase-type. Journal of Applied Probability, 45 (3). pp. 779-799. 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)

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Official URL
http://dx.doi.org/10.1239/jap/1222441829

Abstract

The present paper generalises some results for spectrally negative Levy processes to the setting of Markov additive processes (MAPs). A prominent role is assumed by the first passage times, which will be determined in terms of their Laplace transforms. These have the form of a phase-type distribution, with a rate matrix that can be regarded as an inverse function of the cumulant matrix. A numerically stable iteration to compute this matrix is given. The theory is first developed for MAPs without positive jumps and then extended to include positive jumps having phase-type distributions. Numerical and analytical examples show agreement with existing results in special cases.

Item Type: Article
Uncontrolled keywords: Levy process; first passage time; supremum; Markov additive process; reflected process; stationary distribution
Subjects: Q Science > QA Mathematics (inc Computing science) > QA276 Mathematical statistics
Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Lothar Breuer
Date Deposited: 07 Mar 2009 13:15
Last Modified: 14 Jan 2010 14:14
Resource URI: https://kar.kent.ac.uk/id/eprint/4028 (The current URI for this page, for reference purposes)
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