On stationarity properties of generalized Hermite-type processes

2020/04/30 by Donhauzer, Illia, Olenko, Andriy · 1 citation
#60F17 #60G60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2004.14713

Abstract

The paper investigates properties of generalized Hermite-type processes that arise in non-central limit theorems for integral functionals of long-range dependent random fields. The case of increasing multidimensional domain asymptotics is studied. Three approaches to investigate properties of these processes are discussed. Contrary to the classical one-dimensional case, it is shown that for any choice of a multidimensional observation window the generalized Hermite-type process has non-stationary increments.

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