Rates of clustering for some Gaussian self-similar processes
type: Item
instance of: scholarly article
title: Rates of clustering for some Gaussian self-similar processes
zbMATH Open document ID: 0695.60040
DOI: 10.1007/BF01193582
author: Jim Kuelbs
author: Victor W. Goodman
publication date: 1991-01-01T00:00:00Z
review text: The analogue of Strassen's functional law of the iterated logarithm is known for many Gaussian processes which have suitable scaling properties, and here we establish rates at which this convergence takes place. We provide a new proof of the best upper bound for the convergence to \({\mathcal K}\) by suitably normalized Brownian motion, and then continue with this method to get similar bounds for the Brownian sheet and other self- similar Gaussian processes. The previous method, which produced these results for Brownian motion in \({\mathbb{R}}^ 1\), was highly dependent on many special properties unavailable when dealing with other Gaussian processes.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 4138862
zbMATH Keywords: functional law of the iterated logarithm
zbMATH Keywords: Gaussian processes
zbMATH Keywords: Brownian motion
zbMATH Keywords: Brownian sheet
zbMATH Keywords: self-similar Gaussian processes
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01193582
OpenAlex ID: W2094622812
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4138862