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On the superposition of m-dimensional point processes

Published online by Cambridge University Press:  14 July 2016

Erhan Çinlar
Erhan Çinlar*
Affiliation:
Northwestern University, Evanston, Illinois
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Abstract

Consider n independent vector valued point processes. Superposition is defined component by component as a natural extension of the definition for the one-dimensional case. Under proper conditions as n → ∞, it is shown that the superposed process is a many-dimensional Poisson process with independent components. The results are applied to the superposition of Markov renewal processes.

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Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 1 , April 1968, pp. 169 - 176
Copyright
Copyright © Sheffield: Applied Probability Trust 

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