The laws of iterated and triple logarithms for extreme values of regenerative processes
Open Access
- 17 February 2020
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 7 (1), 61-78
- https://doi.org/10.15559/20-vmsta147
Abstract
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: The laws of iterated and triple logarithms for extreme values of regenerative processes, Authors: Alexander Marynych, Ivan Matsak , We analyze almost sure asymptotic behavior of extreme values of a regenerative process. We show that under certain conditions a properly centered and normalized running maximum of a regenerative process satisfies a law of the iterated logarithm for the lim sup and a law of the triple logarithm for the lim inf. This complements a previously known result of Glasserman and Kou [Ann. Appl. Probab. 5(2) (1995), 424–445]. We apply our results to several queuing systems and a birth and death process.Keywords
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