A note on a limit theorem for differentiable mappings
type: Item
instance of: scholarly article
title: A note on a limit theorem for differentiable mappings
zbMATH Open document ID: 0574.60047
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: A theorem of \textit{C. Hagwood} and \textit{H. Teicher} [Ann. Probab. 11, 1048-1050 (1983; Zbl 0519.60015)] states that the properly normalized random variables \(\max_{k\leq n}k^{-a}(X_ 1+...+X_ n)\) are asymptotically normal. Here \(0\leq a<1\), and \(X_ 1,X_ 2,..\). are i.i.d. random variables with strictly positive mean. The author points out that this and other results follow easily from the observation that under suitable conditions weak convergence of a sequence of random variables is preserved, if a differentiable function is applied to these r.v.
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 3917368
zbMATH Keywords: weak convergence
zbMATH Keywords: mappings
zbMATH Keywords: weak invariance principles
author: K. Borovkov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992924
OpenAlex ID: W2095268694
DOI: 10.1214/AOP/1176992924
description: scientific article; zbMATH DE number 3917368