A note on products of random matrices

Göran Högnäs

Statistics & Probability Letters, 1987, vol. 5, issue 5, 367-370

Abstract: Let P be a probability distribution on a set of d x d matrices. Let Pn denote the n-fold convolution of P with itself. Then tightness of the sequence Pn implies that the Cesáro sequence (1/n[sigma] Pn converges to an idempotent probability measure Q and the support of Q is exactly the set m(S) of matrices of minimal rank in the semigroup S generated by the support of P. Furthermore the set m(S) is a completely simple semigroup with compact group factor. The convergence of Pn can be characterized in terms of the Rees-Suschkewitsch decomposition of m(S).

Keywords: completely; simple; semigroups; minimal; rank; idempotent; probability; measures; tightness; of; matrix; products (search for similar items in EconPapers)
Date: 1987
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(87)90012-5
Full text for ScienceDirect subscribers only

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:eee:stapro:v:5:y:1987:i:5:p:367-370

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().