Renewal shot noise processes in the case of slowly varying tails

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.

arXiv comment8 pages

References in corpus (1)

• Logarithmic scaling of planar random walk's local times

Cited by in corpus (1)

• A functional limit theorem for general shot noise processes