Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 4, Pages 489-496

The structure distribution in a mixed Poisson process

Jozef L. Teugels and Petra Vynckier

JLT, Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, Heverlee, (Leuven) B-3001, Belgium

Received 1 July 1996; Revised 1 October 1996

Copyright © 1996 Jozef L. Teugels and Petra Vynckier. 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.


We use a variety of real inversion formulas to derive the structure distribution in a mixed Poisson process. These approaches should prove to be useful in applications, e.g., in insurance where such processes are very popular.

This article is dedicated to the memory of Roland L. Dobrushin.