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Multidimensional point processes and random closed sets

Published online by Cambridge University Press:  14 July 2016

Michel Baudin
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Abstract

Multidimensional random point processes are shown to be a special case of Matheron's random closed sets. This theory, and in particular Choquet's theorem, are then used to prove a general result on heterogeneous Poisson processes and a uniqueness property of mixed Poisson processes with gamma mixing distributions.

Keywords

CHOQUET'S CAPACITY THEOREM
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 1 , March 1984 , pp. 173 - 178
Copyright
Copyright © Applied Probability Trust 1984 

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References

Fisher, L. (1972) A survey of the mathematical theory of multidimensional point processes. In Stochastic Point Processes, ed. Lewis, P. A. W., Wiley, New York, 468–513.Google Scholar
Kallenberg, O. (1975) Random Measures. Akademie Verlag, Berlin.Google Scholar
Kuznetsov, P. I. and Stratonovich, R. L. (1956) On a mathematical theory of correlated random points. Izv. Akad. Nauk SSSR Ser. Mat. 20, 167–178.Google Scholar
Matheron, G. (1967) Elements pour un théorie des milieux poreux. Masson, Paris.Google Scholar
Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar
MoYal, J. E. (1962) The general theory of stochastic population processes. Acta Math. 108, 1–31.CrossRefGoogle Scholar
Stapper, C. H., Mclaren, A. N. and Dreckmann, M. (1980) Yield model for productivity optimization of VLSI memory chips with redundancy and partially good product. IBM J. Res. Devel. 24, 398–409.CrossRefGoogle Scholar