On central limit theorems in probability gage spaces
type: Item
instance of: scholarly article
title: On central limit theorems in probability gage spaces
zbMATH Open document ID: 0593.60037
author: G. O. S. Ekhaguere
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1985-01-01T00:00:00Z
review text: A probability gage space over a semi-finite \(W^*\)-algebra is considered as a non-commutative or quantum analogue of the classical probability space. In this setting some limit theorems are proved and, in particular a Levy-Khinchine type of representation for the Fourier transforms of limit probability gages is established. The results are obtained by exploiting some of the algebraic and topological properties of certain set of operators called the decomposability algebraic structures, associated with probability gages. Reviewer's remark: Another approach to central limit theorems in non- commutative probability theory is given in papers of \textit{B. G. Gol'dsthejn} [e.g. Teor. Veroyatn. Primen. 27, No.4, 657-666 (1982; Zbl 0506.46048); English translation in Theory Probab. Appl. 27, 703-714 (1982)].
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 3953957
zbMATH Keywords: gage space
zbMATH Keywords: Levy-Khinchine type of representation
zbMATH Keywords: Fourier transforms
zbMATH Keywords: non-commutative probability theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195179056
OpenAlex ID: W2148116722
DOI: 10.2977/PRIMS/1195179056
description: scientific article; zbMATH DE number 3953957