A fixed point theorem and its application to the central limit theorem
type: Item
instance of: scholarly article
title: A fixed point theorem and its application to the central limit theorem
zbMATH Open document ID: 0553.60028
DOI: 10.1007/BF01247572
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: At first, the authors introduce a metric on a space of distribution functions and then define a self-mapping of this space which is proved to be contractive. Subsequently, the authors use their fixed point result to give a proof of the central limit theorems for sequences of sub- independent identically distributed random variables. A similar idea was used by \textit{H. F. Trotter} [Arch. Math. 10, 226-234 (1959; Zbl 0086.340)] to give a proof of the central limit theorem. Although he gives a proof in which the use of characteristic functions is avoided, this will limit his result to the case of independent random variables. The approach in this paper is considerably different and the result requires only the weaker assumption of sub-independence.
reviewed by: Kun-Jen Chung
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 3881577
zbMATH Keywords: metric on a space of distribution functions
zbMATH Keywords: central limit theorems
zbMATH Keywords: sub- independence
Wikidata QID: Q59884375
author: G. G. Hamedani
author: Gilbert G. Walter
MaRDI profile type: Publication
cites work: Q5512264
cites work: An elementary proof of the central limit theorem
cites work: Q5836235
full work available at URL: https://doi.org/10.1007/bf01247572
OpenAlex ID: W2040341059
description: scientific article; zbMATH DE number 3881577