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Theory of Stochastic Processes, 2016, Volume 21(37), Issue 2, Pages 14–21 (Mi thsp159)  
Renewal shot noise processes in the case of slowly varying tails

Zakhar Kabluchkoa, Alexander Marynychb

a Institut für Mathematische Statistik, Westfälische Wilhelms-Universität Münster, Orléans–Ring 10, 48149 Münster, Germany
b Faculty of Cybernetics, Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine
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Abstract: We investigate weak convergence of renewal shot noise processes in the case of slowly varying tails of the inter-shot times. We show that these processes, after an appropriate non-linear scaling, converge in the sense of finite-dimensional distributions to an inverse extremal process.
Keywords: Extremal process, random process with immigration, renewal theory, shot noise process.
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Document Type: Article
MSC: Primary 60F05; Secondary 60K05
Language: English
Citation: Zakhar Kabluchko, Alexander Marynych, “Renewal shot noise processes in the case of slowly varying tails”, Theory Stoch. Process., 21(37):2 (2016), 14–21
Citation in format AMSBIB
\Bibitem{KabMar16}
\by Zakhar Kabluchko, Alexander Marynych
\paper Renewal shot noise processes in the case of slowly varying tails
\jour Theory Stoch. Process.
\yr 2016
\vol 21(37)
\issue 2
\pages 14--21
\mathnet{http://mi.mathnet.ru/thsp159}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3662592}
\zmath{https://zbmath.org/?q=an:1374.60174}
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