Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 367170, 14 pages
The Distribution of the Interval between Events of a Cox Process with Shot Noise Intensity
1Department of Statistics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK
2Division of Economic and Financial Studies, Department of Actuarial Studies, Macquarie University, Sydney NSW 2109, Australia
Received 19 June 2008; Accepted 19 September 2008
Academic Editor: Enzo Orsingher
Copyright © 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.
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.