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Superimposed non-stationary renewal processes

Published online by Cambridge University Press:  14 July 2016

S. Blumenthal ,
J. A. Greenwood  and
L. Herbach
S. Blumenthal
Affiliation:
New York University
J. A. Greenwood
Affiliation:
New York University
L. Herbach
Affiliation:
New York University
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Extract

For superposition of independent, stationary renewal processes, it is well known that the distribution of waiting time between events for the superimposed process is approximately exponential if the number of processes involved is sufficiently large, (see Khintchine (1960), Ososkov (1956)). We assume that all component processes have the same age t, and we generalize the classical result to show that even for t finite (non-stationary case), the limiting waiting time distribution (as the number of processes increases) is exponential with a scale parameter which depends on t through the average of the individual process renewal densities.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 1 , March 1971 , pp. 184 - 192
Copyright
Copyright © Applied Probability Trust 1971 

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