Limit theorems for filtered long-range dependent random fields

2018/12/18 by Alodat, Tareq, Leonenko, Nikolai, Olenko, Andriy
#60F05 #60F17 #60G35 #60G60 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1812.07290

Abstract

This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of long-range dependent fields and increasing observation windows is studied. The obtained limit random processes are non-Gaussian. Most known results on this topic give asymptotic processes that always exhibit non-negative auto-correlation structures and have the self-similar parameter H∈((1)/(2),1). In this work we also obtain convergence for the case H∈(0,(1)/(2)) and show how the Hurst parameter H can depend on the shape of the observation windows. Various examples are presented.

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