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Interparticle dependence in a linear death process subjected to a random environment

Published online by Cambridge University Press:  14 July 2016

Claude Lefèvre and
György Michaletzky
Claude Lefèvre*
Affiliation:
Université de Bruxelles
György Michaletzky*
Affiliation:
University Eötvös L.
*
∗ Postal address: Université Libre de Bruxelles, Institut de Statistique, C.P. 210, Boulevard du Triomphe, B-1050 Bruxelles, Belgium.
∗∗ Postal address: University Eötvös L., Department of Probability Theory and Statistics, 1088 Muzeum Krt 6-8, Budapest, VIII ker, Hungary.
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Abstract

Recently, Ball and Donnelly (1987) investigated the nature of the interparticle dependence in a death process with non-linear rates. In this note, after some remarks on their result, a similar problem is examined for a linear death process where the death rate per particle is a monotone function of the current state of a random environment. It is proved that if the exterior process involved is a homogeneous birth-and-death process valued in ℕ, then the survival times of any subset of particles are positively upper orthant dependent. A simple example shows that this property is not valid for general exterior processes.

Keywords

RISK-SHARING SYSTEMBIRTH-AND-DEATH ENVIRONMENTWEISS EPIDEMIC MODELUPPER ORTHANT DEPENDENT VARIABLESASSOCIATED VARIABLES

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990, pp. 491 - 498
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

This research was partially supported by a grant of the Belgium F.N.R.S.

The paper was written while the authors were visting the Statistics and Applied Probability Program, University of California, Santa Barbara.

References

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