A Hanson-Russo-type law of the iterated logarithm for fractional Brownian motion
type: Item
instance of: scholarly article
title: A Hanson-Russo-type law of the iterated logarithm for fractional Brownian motion
zbMATH Open document ID: 0770.60030
DOI: 10.1016/0167-7152(93)90190-T
author: Charles El-Nouty
published in: Statistics \& Probability Letters
publication date: 1993-05-24T00:00:00Z
review text: Let \(\{B_ H(t),\;t\geq 0\}\) be a fractional Brownian motion of index \(H\) and consider its increments \(X_ n(u)=\beta_ n(B_ H(n+ug(n))-B_ H(n))\) \((0\leq u\leq 1)\) with a given increment function \(g(n)\) and a suitable normalizing factor \(\beta_ n\). The author proves that the set of the limit points of \(X_ n(\cdot)\) \((n\to\infty)\) is a natural generalization of the Strassen class.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 178026
zbMATH Keywords: law of iterated logarithm
zbMATH Keywords: path properties
zbMATH Keywords: fractional Brownian motion
reviewed by: Pál Révész
MaRDI profile type: Publication
cites work: On large intervals in the Cs�rg?-R�v�sz theorem on increments of a Wiener process
cites work: Answers to some questions about increments of a Wiener process
cites work: How big are the increments of a Wiener process?
cites work: Some results on increments of the Wiener process with applications to lag sums of i.i.d. random variables
cites work: Some more results on increments of the Wiener process
cites work: Some ``lim inf'' results for increments of a Wiener process
cites work: Q5676871
cites work: Reproducing kernel Hilbert spaces and the law of the iterated logarithm for Gaussian processes
cites work: On strassen-type laws of the iterated logarithm for gaussian elements in abstract spaces
cites work: Upper classes for the increments of fractional Wiener processes
cites work: A generalization of Strassen's functional law of iterated logarithm
cites work: An invariance principle for the law of the iterated logarithm
cites work: Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence
cites work: A survey of functional laws of the iterated logarithm for self-similar processes
full work available at URL: 0167-7152(93)90190-t
OpenAlex ID: W2064248006
Recommended article: Q3526633
Recommended article: An Erdös-Révész type law of the iterated logarithm for reflected fractional Brownian motion
Recommended article: Strassen-type Laws of Iterated Logarithm for a Fractional Brownian Sheet
Recommended article: Chung's functional law of the iterated logarithm for increments of a fractional Brownian motion
Recommended article: Q3154279
Recommended article: A law of iterated logarithm for the subfractional Brownian motion and an application
Recommended article: Laws of the iterated logarithm for \(\alpha\)-time Brownian motion
Recommended article: Q4347637
Recommended article: Q3697980
description: scientific article; zbMATH DE number 178026