Maxima of linear processes with heavy-tailed innovations and random coefficients

TL;DR

This paper studies the behavior of maximum values in linear processes driven by heavy-tailed innovations and random coefficients, establishing their convergence properties using advanced probabilistic techniques.

Contribution

It introduces a novel approach to analyze the maxima of such processes, deriving functional convergence in the Skorohod M1 topology.

Findings

Established functional convergence of partial maxima processes

Applied point process approach to heavy-tailed linear processes

Extended understanding of maxima behavior in complex stochastic models

Abstract

We investigate maxima of linear processes with i.i.d. heavy-tailed innovations and random coefficients. Using the point process approach we derive functional convergence of the partial maxima stochastic process in the space of non-decreasing c\`{a}dl\`{a}g functions on $[0,1]$ with the Skorohod $M_{1}$ topology.