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.
(doi:10.1239/jap/1222441829)
(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:4028)

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. | |

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 |
---|---|

DOI/Identification number: | 10.1239/jap/1222441829 |

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: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | Lothar Breuer |

Date Deposited: | 07 Mar 2009 13:15 UTC |

Last Modified: | 16 Nov 2021 09:42 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/4028 (The current URI for this page, for reference purposes) |

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