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A comparison criterion for explosions in point processes

Published online by Cambridge University Press:  14 July 2016

J. Haezendonck  and
F. de Vylder
J. Haezendonck*
Affiliation:
University of Antwerp
F. de Vylder*
Affiliation:
Université Catholique de Louvain
*
∗Postal address: Department of Mathematics, University of Antwerp, Universiteitsplein 1, B–2610 Wilryk, Belgium.
∗∗Postal address: Université Catholique de Louvain, 1348 Louvain-La-Neuve, Belgium
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Abstract

It is proved that under certain conditions the probability of explosion of a first point process is not larger than the probability of explosion of a second point process if the intensities of both processes fulfil the same inequality.

Keywords

POINT PROCESSEXPLOSIONRANDOM INTENSITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 1102 - 1107
Copyright
Copyright © Applied Probability Trust 

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References

[1] Bühlmann, H. (1970) Mathematical Methods in Risk Theory. Springer-Verlag, Berlin.Google Scholar
[2] De Vylder, F. (1977) Martingales and ruin in a dynamical risk process. Scand. Actuarial J., 217–225.Google Scholar