The rate of convergence in the functional central limit theorem for random quadratic forms with some applications to the law of the iterated logarithm
type: Item
instance of: scholarly article
title: The rate of convergence in the functional central limit theorem for random quadratic forms with some applications to the law of the iterated logarithm
zbMATH Open document ID: 0685.60034
DOI: 10.1007/BF01300920
author: T. Mikosch
published in: Monatshefte für Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178418
review text: Applying Skorokhod embedding techniques we prove a convergence rate in the functional central limit theorem for quadratic forms in independent random variables which satisfy a fourth moment condition. Using this result we get a law of the iterated logarithm as well as an analogue of Chung's law of the iterated logarithm for random quadratic forms.
reviewed by: T. Mikosch
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60G42
zbMATH DE Number: 4122961
zbMATH Keywords: Skorokhod embedding techniques
zbMATH Keywords: convergence rate
zbMATH Keywords: functional central limit theorem
zbMATH Keywords: law of the iterated logarithm
MaRDI profile type: Publication
cites work: Q5560061
cites work: Q3657121
cites work: Convergence of quadratic forms in p-stable random variables and \(\theta _ p\)-radonifying operators
cites work: Q3911791
cites work: A central limit theorem for generalized quadratic forms
cites work: Q3661731
cites work: Q3774636
cites work: Bounded laws of the iterated logarithm for quadratic forms in Gaussian random variables
cites work: Functional limit theorems for random quadratic forms
cites work: Moment inequalities and the strong laws of large numbers
cites work: Q4085018
cites work: Q4084474
Recommended article: Functional limit theorems for random quadratic forms
Recommended article: Q3719562
Recommended article: Bounded laws of the iterated logarithm for quadratic forms in Gaussian random variables
Recommended article: Functional central limit theorem and Strassen's law of the iterated logarithms for weakly multiplicative systems
Recommended article: Q3761396
Recommended article: Q4468970
Recommended article: Q3539594
description: scientific article; zbMATH DE number 4122961