Continuous Singularity of the Weak Limit of Convolution Powers of a Discrete Probability Measure on 2 × 2 Stochastic Matrices

A. Mukherjea and J. S. Ratti
Additional contact information
A. Mukherjea: University of South Florida
J. S. Ratti: University of South Florida

Journal of Theoretical Probability, 1997, vol. 10, issue 2, 499-506

Abstract: Abstract Let μ be a probability measure on n 2 × 2 stochastic matrices, n an arbitrary positive integer, and λ= (w) lim n→∞ μ n , such that the support of λ consists of 2 × 2 stochastic matrices of rank one, and as such, λ can be regarded as a probability measure on [0, 1]. We present simple sufficient conditions for λ to be continuous singular w.r.t. the Lebesgue measure on [0, 1]. We also determine λ, given μ.

Keywords: Convolution; random matrices; weak convergence (search for similar items in EconPapers)
Date: 1997
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1023/A:1022672802749 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:10:y:1997:i:2:d:10.1023_a:1022672802749

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1022672802749

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().