On the continuous singularity of the limit distribution of products of i. i. d. \(d\times d\) stochastic matrices
type: Item
instance of: scholarly article
title: On the continuous singularity of the limit distribution of products of i. i. d. \(d\times d\) stochastic matrices
zbMATH Open document ID: 1018.60035
DOI: 10.1023/A:1020636603528
author: A. Mukherjea
author: Anastase Nakassis
published in: Journal of Theoretical Probability
publication date: 2003-04-03T00:00:00Z
review text: In generalizing earlier results [cp. e.g. \textit{T.-C. Sun}, Bull. Inst. Math., Acad. Sin. 3, 235-248 (1975; Zbl 0327.60009); \textit{A. Nakassis}, J. Math. Anal. Appl. 70, 337-347 (1979; Zbl 0426.60012); and the authors and \textit{J. S. Ratti}, J. Theor. Probab. 12, No.~2, 571-583 (1999; Zbl 0943.60010) and ibid. 12, No.~4, 1109-1112 (1999; Zbl 0961.60014)] the authors give sufficient conditions for the limit distribution of products of i.i.d. \(d\times d\) random stochastic matrices, \(d\) finite and \(d\geq 2\), to be continuous singular, when the support of the distribution of the individual random matrices is finite or countably infinite. The proofs are based on applications of the multivariate central limit theorem. The references contain ten bibliographical hints.
reviewed by: Ludwig Paditz
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 60B99
zbMATH DE Number: 1892251
zbMATH Keywords: random matrices
zbMATH Keywords: limit distribution
zbMATH Keywords: central limit theorem
zbMATH Keywords: Erdős problem
zbMATH Keywords: Cantor function
zbMATH Keywords: continuous singularity
zbMATH Keywords: product of independent identically distributed stochastic matrices
MaRDI profile type: Publication
full work available at URL: a:1020636603528
OpenAlex ID: W52295150
description: scientific article; zbMATH DE number 1892251