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On a Property of Finite-State Birth and Death Processes
A. J. Branford
Journal of Applied Probability
Vol. 23, No. 4 (Dec., 1986), pp. 859-866
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3214460
Page Count: 8
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A simple proof is given of the result that the `overflow' from a finite-state birth and death process is a renewal stream characterized by hyperexponential inter-event times. Our structure is utilized to give a converse result that any hyperexponential renewal stream can be so produced as the overflow from a finite-state birth and death process.
Journal of Applied Probability © 1986 Applied Probability Trust