A note on the almost sure approximation of weakly dependent random variables
type: Item
instance of: scholarly article
title: A note on the almost sure approximation of weakly dependent random variables
zbMATH Open document ID: 0602.60008
DOI: 10.1007/BF01294601
author: Walter Philipp
published in: Monatshefte für Mathematik
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178301
review text: A strong approximation theorem for Hilbert space valued martingales, due to \textit{G. J. Morrow} and the author [see Trans. Am. Math. Soc. 273, 231- 251 (1982; Zbl 0508.60014)], is improved. This result is then used to strengthen and, at the same time, to extend a recent strong approximation theorem for weakly dependent \({\mathbb{R}}^ d\)-valued random variables, due to \textit{E. Eberlein} [see Probability in Banach spaces IV, Proc. Semin., Oberwolfach 1982, Lect. Notes Math. 990, 84-91 (1983; Zbl 0515.60027)], to Hilbert space valued random variables.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 3971859
zbMATH Keywords: almost sure approximation of weakly dependent random variables
zbMATH Keywords: strong approximation theorem
zbMATH Keywords: Hilbert space valued martingales
MaRDI profile type: Publication
cites work: On strong invariance principles under dependence assumptions
cites work: Q3911791
cites work: Almost sure invariance principles for partial sums of mixing B-valued random variables
cites work: A weak invariance principle for Hilbert space valued martingales
cites work: An almost sure Invariance Principle for Hilbert Space Valued Martingales
cites work: Almost sure invariance principles for partial sums of weakly dependent random variables
cites work: Contributions to Central Limit Theory for Dependent Variables
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description: scientific article; zbMATH DE number 3971859