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High-Level exceedances of regenerative and semi-stationary processes

Published online by Cambridge University Press:  14 July 2016

Richard Serfozo
Richard Serfozo*
Affiliation:
Bell Laboratories
*
∗Postal address: Bell Laboratories, WB–1G 306, Holmdel, N.J. 07733, U.S.A.
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Abstract

The cumulative amount of time that a regenerative or semi-stationary process exceeds a high level and other measures of these exceedances are considered as special cases of a non-decreasing stochastic process of partial sums. We present necessary and sufficient conditions for these exceedance processes to converge in distribution to Poisson processes or processes with stationary independent non-negative increments as the level goes to infinity. We apply our results to random walks, M/M/s queues, and thinnings of point processes.

Keywords

HIGH-LEVEL EXCEEDANCESMARKOV CHAINSREGENERATIVE PROCESSESSEMI-STATIONARY PROCESSESWEAK CONVERGENCEM/M/s QUEUETHINNING OF POINT PROCESSES
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 423 - 431
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Part of this research was done at Syracuse University under the sponsorship of Air Force Office of Scientific Research Grant #AFOSR–74–2627, and National Science Foundation Grant #ENG75–13653.

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