Renewal shot noise processes in the case of slowly varying tails

Zakhar Kabluchko^a, Alexander Marynych<sup>b

a</sup> 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

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.

MSC: Primary 60F05; Secondary 60K05

Language: English

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