CONVERGENCE IN DISTRIBUTION OF PRODUCTS OF IID-NONNEGATIVE-MATRICES

Authors
DHAR S MUKHERJEA A
Citation
S. Dhar et A. Mukherjea, CONVERGENCE IN DISTRIBUTION OF PRODUCTS OF IID-NONNEGATIVE-MATRICES, Journal of theoretical probability, 10(2), 1997, pp. 375-393
Citations number
8
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Journal of theoretical probability → ACNP
ISSN journal
08949840
Volume
10
Issue
2
Year of publication
1997
Pages
375 - 393
Database
ISI
SICI code
0894-9840(1997)10:2<375:CIDOPO>2.0.ZU;2-3
Abstract
Let (X-i) be a sequence of m x m i.i.d. stochastic matrices with distr ibution mu. Then mu(n) is the distribution of XnXn-1 ... X-1. Simple s ufficient conditions for the weak convergence of (u(n)) are presented here. An extremely simple land verifiable) necessary and sufficient co ndition is provided for m = 3. The method for m = 3 works for m > 3 ev en though calculations are more involved for higher values of m. We al so discuss the purity of the limit distribution for m greater than or equal to 2.