Renewal shot noise processes in the case of slowly varying tails

2016/05/09 by Kabluchko, Zakhar, Marynych, Alexander · 1 citation
#60F05 (Primary) #60K05 (Secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1605.02659

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.

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