Hostname: page-component-6bb9c88b65-vqtzn Total loading time: 0 Render date: 2025-07-25T19:36:02.714Z Has data issue: false hasContentIssue false
  • English
  • Français

On conditional intensities and on interparticle correlation in non-linear death processes

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Timothy C. Brown  and
Peter Donnelly
Timothy C. Brown
Affiliation:
University of Western Australia
Peter Donnelly*
Affiliation:
Queen Mary and Westfield College, London
*
∗∗Postal address: School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Ball and Donnelly (1987) announced a result giving circumstances in which there is positive or negative correlation between the death times in a non-linear, Markovian death process. A proof is provided here, based on results concerning the distribution of optional random variables in terms of their conditional intensities.

Keywords

CORRELATIONMARTINGALE

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces

Information

Type
Letter to the Editor
Information
Advances in Applied Probability , Volume 25 , Issue 1 , March 1993 , pp. 255 - 260
Copyright
Copyright © Applied Probability Trust 1993 

Footnotes

∗

Present address: Department of Statistics, University of Melbourne, Parkville, VIC 3052, Australia.

References

Ball, F. and Donnelly, P. (1987) Interparticle correlation in death processes with application to variability in compartmental models. Adv. Appl. Prob. 18, 755–766.Google Scholar
Brémaud, P. (1981) Point Processes and Queues: Martingale Dynamics. Springer-Verlag, Berlin.Google Scholar
Donnelly, P. (1993) The correlation structure of epidemic models. To appear.Google Scholar
Faddy, M. J. (1985) Non-linear stochastic compartmental models. IMA J. Math. Appl. Med. Biol. 2, 287–297.Google Scholar
Karlin, S. and Mcgregor, J. L. (1959) Coincidence probabilities. Pacific J. Math. 9, 1141–1164.Google Scholar
Karlin, S. and Rinott, Y. (1980) Classes of orderings of measures and related correlation inequalities. 1. Multivariate totally positive distributions. J. Multivariate Anal. 10, 467–498.Google Scholar
Lefevre, C. and Michaletzky, G. (1990) Interparticle dependence in a linear death process subjected to a random environment. J. Appl. Prob. 27, 491–498.Google Scholar
Lefevre, C. and Milhaud, X. (1990) On the association of the lifelengths of components subjected to a stochastic environment. Adv. Appl. Prob. 22, 961–964.Google Scholar
Melamed, B. and Walrand, J. (1986) On the one-dimensional distribution of counting processes with stochastic intensities. Stochastics 19, 1–9.Google Scholar