The law of the iterated logarithm for non-instantaneous filters of strongly dependent Gaussian sequences
type: Item
instance of: scholarly article
title: The law of the iterated logarithm for non-instantaneous filters of strongly dependent Gaussian sequences
zbMATH Open document ID: 0832.60041
DOI: 10.1007/BF02212883
author: Hwai-Chung Ho
published in: Journal of Theoretical Probability
publication date: 1995-05-23T00:00:00Z
review text: Let \(\{X_n\}\) be a stationary Gaussian sequence, \(H = H(X_{t_1}, \ldots, X_{t_d})\) a \(d\)-dimensional filter with mean zero, \(\theta\) the shift operator and \(S_N = \sum^N_1 H \circ \theta^n\). It is shown that the upper-half law of the iterated logarithm holds for \(S_N\) under suitable conditions on the Hermite rank of \(H\) and the covariance function of \(\{X_n\}\).
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60J55
zbMATH DE Number: 757600
zbMATH Keywords: Hermite rank
zbMATH Keywords: upper class test
zbMATH Keywords: stationary Gaussian sequence
zbMATH Keywords: law of the iterated logarithm
reviewed by: Søren Asmussen
MaRDI profile type: Publication
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cites work: Q3290160
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full work available at URL: https://doi.org/10.1007/bf02212883
OpenAlex ID: W1985641825
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description: scientific article; zbMATH DE number 757600