Extremes of Shot-Noise Fields in the Presence of Regularly Varying Tails with Index $\boldsymbol{\alpha\in(0,1)}$

Abstract

The paper considers shot-noise fields with regularly varying tail amplitudes with index $\alpha\in (0,1)$. The asymptotic behavior of the supreme of the field over bounded measurable regions growing in the van Hove sense is investigated. The nondegenerate limit law, which was obtained earlier by the author, will be deduced under other assumptions.