Renewal shot noise processes in the case of slowly varying tails

Zakhar Kabluchko, Alexander Marynych
Theory of Stochastic Processes
Vol.21 (37), no.2, 2016, pp.14-21
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.