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Limit theorems for thinning of renewal point processes

Published online by Cambridge University Press:  14 July 2016

Råde L.*
Affiliation:
Chalmers University of Technology, Gothenburg, Sweden

Abstract

Limit theorems for the thinning of renewal point processes according to two different schemes are studied. In the first scheme when a point is retained a random number of succeeding points are deleted. According to the second scheme a random number of points are deleted by an inhibitory Poisson process.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Coleman, R. and Gastwirth, J. L. (1969) Some models for interaction of renewal processes related to neuron firing. J. Appl. Prob. 6, 3858.CrossRefGoogle Scholar
[2] Gnedenko, B. V. and Kovalenko, I. N. (1968) Introduction to Queueing Theory. Israel Program for Scientific Translations, Jerusalem.Google Scholar
[3] Rényi, A. (1956) A Poisson-folyamat egy jellemzése (A characterization of the Poisson process). Proc. Math. Inst. Hungarian Acad. Sci. I, 519527.Google Scholar
[4] Råde, L. (1972) A model for interaction of a Poisson and a renewal process and its relation with queuing theory. J. Appl. Prob. 9, 451456.CrossRefGoogle Scholar
[5] Ten Hoopen, M. and Reuver, H. (1965) Selective interaction of two independent recurrent processes. J. Appl. Prob. 2, 286292.CrossRefGoogle Scholar