Zakhar Kabluchko, Alexander Marynych, “Renewal shot noise processes in the case of slowly varying tails”, Theory Stoch. Process., 2016, том 21(37), выпуск 2,страницы 14

Renewal shot noise processes in the case of slowly varying tails

Zakhar Kabluchko^a, Alexander Marynych^b

^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

Аннотация: 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.

Ключевые слова: Extremal process, random process with immigration, renewal theory, shot noise process.

MSC: Primary 60F05; Secondary 60K05

Язык публикации: английский