Convergence in Distribution of Products of I.I.D. Nonnegative Matrices

S. Dhar () and A. Mukherjea ()
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S. Dhar: University of South Florida
A. Mukherjea: University of South Florida

Journal of Theoretical Probability, 1997, vol. 10, issue 2, 375-393

Abstract: Abstract Let (X i) be a sequence of m × m i.i.d. stochastic matrices with distribution μ. Then μ n is the distribution of X n X n−1 ...X 1. Simple sufficient conditions for the weak convergence of (μ n ) are presented here. An extremely simple (and verifiable) necessary and sufficient condition is provided for m= 3. The method for m= 3 works for m> 3 even though calculations are more involved for higher values of m. We also discuss the purity of the limit distribution for m≥2.

Keywords: Random matrices; convergence in distribution; weak convergence (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022612516862

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