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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
DOI: 10.2307/3214460
Stable URL: http://www.jstor.org/stable/3214460
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 a Property of Finite-State Birth and Death Processes
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Abstract

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.

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