High-Level exceedances of regenerative and semi-stationary processes
Keyword(s):
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.
1980 ◽
Vol 17
(02)
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pp. 423-431
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1972 ◽
Vol 4
(01)
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pp. 151-176
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1993 ◽
Vol 30
(04)
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pp. 877-888
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1976 ◽
Vol 13
(03)
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pp. 519-529
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2016 ◽
Vol 374
(2058)
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pp. 20150099
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