Rates of convergence for the functional LIL
type: Item
instance of: scholarly article
title: Rates of convergence for the functional LIL
zbMATH Open document ID: 0672.60011
published in: The Annals of Probability
publication date: 1989-01-01T00:00:00Z
review text: Let \(X,X_ 1,X_ 2,..\). be i.i.d. random variables such that E X\(=0\), E \(X^ 2=1\). Let S(t), \(t\geq 0\), be the polygonal process. The rate of convergence of the random sequence \[ \{S(n(\cdot))/(2n LL n)^{1/2},\quad n\geq 1\} \] to a compact convex symmetric subset of C[0,1] is obtained. Under additional assumptions, the same result has earlier been proved by the authors in J. Theor. Probab. 1, 27-63 (1988; Zbl 0651.60039).
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 4100268
zbMATH Keywords: rate of convergence
author: Victor W. Goodman
author: Jim Kuelbs
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991510
OpenAlex ID: W2029539341
DOI: 10.1214/AOP/1176991510
description: scientific article; zbMATH DE number 4100268