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Renewal shot noise processes in the case of slowly varying tails. (English) Zbl 1374.60174
Summary: 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.

MSC:
60K05 Renewal theory
60F05 Central limit and other weak theorems
60G70 Extreme value theory; extremal stochastic processes
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