The distribution of the interval between events of a Cox process with shot noise intensity
type: Item
instance of: scholarly article
title: The distribution of the interval between events of a Cox process with shot noise intensity
zbMATH Open document ID: 1159.60304
DOI: 10.1155/2008/367170
author: Angelos Dassios
author: Ji-Wook Jang
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2009-04-01T00:00:00Z
full work available at URL: https://eudml.org/doc/55294
review text: Summary: 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.
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60K05
zbMATH DE Number: 5538664
Wikidata QID: Q58645908
MaRDI profile type: Publication
OpenAlex ID: W1984744353
cites work: Explosive Poisson shot noise processes with applications to risk reserves
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description: scientific article; zbMATH DE number 5538664