Sample behavior of some random series
type: Item
instance of: scholarly article
title: Sample behavior of some random series
zbMATH Open document ID: 0882.60004
DOI: 10.1007/BF02214264
author: Geoffrey Pritchard
published in: Journal of Theoretical Probability
publication date: 1998-02-18T00:00:00Z
review text: Let \(\{X_j\}^\infty_{j=1}\) be a sequence of i.i.d. real-valued random variables and \(V_1\), \(V_2, \dots\) be fixed vectors in Banach space \(E\). The scaled-sample property \((\{X^{(j)}/ \gamma_n\}^n_{j=1} \to k\) a.s. as \(n\to \infty\), where \(\gamma_n>0\) and \(X^{(j)}\) are i.i.d. with law \(\mu)\) is investigated for distributions \(\mu\) which are the laws of random series of the form \(\sum^\infty_{j=1} X_jV_j\). The main result establishes this convergence for a large collection of possible distributions \(\mu\) including some discrete examples.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 1018712
zbMATH Keywords: scale sample
zbMATH Keywords: random series
zbMATH Keywords: laws of random series
reviewed by: N. G. Gamkrelidze
MaRDI profile type: Publication
cites work: Q4726487
cites work: Some deviation inequalities
cites work: On the convergence of scaled random samples
cites work: Q4037241
description: scientific article; zbMATH DE number 1018712