The laws of iterated and triple logarithms for extreme values of regenerative processes

The laws of iterated and triple logarithms for extreme values of regenerative processes

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 t...

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Main Authors: Alexander Marynych, Ivan Matsak
Format: Article
Language:English
Published: VTeX 2020-02-01
Series:Modern Stochastics: Theory and Applications
Subjects:
Extreme values
regenerative processes
queuing systems
Online Access:https://www.vmsta.org/doi/10.15559/20-VMSTA147
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spelling doaj-b77b5e0c7a274ca890942f31347a39352020-11-25T02:04:40ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542020-02-0171617810.15559/20-VMSTA147The laws of iterated and triple logarithms for extreme values of regenerative processesAlexander Marynych0Ivan Matsak1Taras Shevchenko National University of Kyiv, Faculty of Computer Science and Cybernetics, 01601 Kyiv, UkraineTaras Shevchenko National University of Kyiv, Faculty of Computer Science and Cybernetics, 01601 Kyiv, UkraineWe 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.https://www.vmsta.org/doi/10.15559/20-VMSTA147Extreme valuesregenerative processesqueuing systems
collection DOAJ
language English
format Article
sources DOAJ
author Alexander Marynych
Ivan Matsak
spellingShingle Alexander Marynych
Ivan Matsak
The laws of iterated and triple logarithms for extreme values of regenerative processes
Modern Stochastics: Theory and Applications
Extreme values
regenerative processes
queuing systems
author_facet Alexander Marynych
Ivan Matsak
author_sort Alexander Marynych
title The laws of iterated and triple logarithms for extreme values of regenerative processes
title_short The laws of iterated and triple logarithms for extreme values of regenerative processes
title_full The laws of iterated and triple logarithms for extreme values of regenerative processes
title_fullStr The laws of iterated and triple logarithms for extreme values of regenerative processes
title_full_unstemmed The laws of iterated and triple logarithms for extreme values of regenerative processes
title_sort laws of iterated and triple logarithms for extreme values of regenerative processes
publisher VTeX
series Modern Stochastics: Theory and Applications
issn 2351-6046
2351-6054
publishDate 2020-02-01
description 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.
topic Extreme values
regenerative processes
queuing systems
url https://www.vmsta.org/doi/10.15559/20-VMSTA147
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