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On the Superposition of m-Dimensional Point Processes

Erhan Çinlar
Journal of Applied Probability
Vol. 5, No. 1 (Apr., 1968), pp. 169-176
DOI: 10.2307/3212084
Stable URL: http://www.jstor.org/stable/3212084
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Superposition of m-Dimensional Point Processes
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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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