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Modes of growth of counting processes with increasing arrival rates

Published online by Cambridge University Press:  14 July 2016

W. A. O'N. Waugh
W. A. O'N. Waugh*
Affiliation:
The University of Toronto
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Abstract

Jumping processes which grow by unit jumps, with decreasing sojourn times between successive jumps, are studied. Markovian birth processes, non-Markovian branching processes, and some generalizations of these are special cases. Three classes are described, in one of which growth is explosive, in the second asymptotically continuous, and in the third oscillatory. A theorem is proved which gives an explicit functional expression in the asymptotically continuous case, and borderline cases between the classes are investigated.

Keywords

COUNTING PROCESSESBIRTH PROCESSESBRANCHING PROCESSESSOJOURN TIMESFIRST ENTRY TIMESNON-MARKOVIAN GROWTHASYMPTOTIC GROWTH
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 237 - 247
Copyright
Copyright © Applied Probability Trust 1974 

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