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

By Angelos Dassios and Jiwook Jang

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

Topics: HA Statistics
Publisher: Hindawi Publishing Corporation
Year: 2008
DOI identifier: 10.1155/2008
OAI identifier: oai:eprints.lse.ac.uk:31864
Provided by: LSE Research Online

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