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

Angelos Dassios, Jiwook Jang*

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish
Article number367170
Pages (from-to)1-14
Number of pages14
JournalJournal of Applied Mathematics and Stochastic Analysis
Volume2008
DOIs
Publication statusPublished - 2008

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