The distribution of the interval between events of a Cox process with shot noise intensity

Dassios, Angelos ORCID: 0000-0002-3968-2366 and Jang, Jiwook (2008) The distribution of the interval between events of a Cox process with shot noise intensity. Journal of Applied Mathematics and Stochastic Analysis, 2008. pp. 1-14. ISSN 1048-9533

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Abstract

Applying piecewise deterministic Markov processes theory, the probability generating function of a Cox process, incorporating with shot noise process as the claim intensity, is obtained. We also derive the Laplace transform of the distribution of the shot noise process at claim jump times, using stationary assumption of the shot noise process at any times. Based on this Laplace transform and from the probability generating function of a Cox process with shot noise intensity, we obtain the distribution of the interval of a Cox process with shot noise intensity for insurance claims and its moments, that is, mean and variance.

Item Type:	Article
Official URL:	http://www.hindawi.com/journals/ijsa/
Additional Information:	© 2008 Angelos Dassios and Jiwook Jang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Hardcopy ISSN: 1048-9533.
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	28 Jan 2011 15:18
Last Modified:	11 Dec 2024 23:22
URI:	http://eprints.lse.ac.uk/id/eprint/31864

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