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

Author

Listed:
  • S. Dhar

    (University of South Florida)

  • A. Mukherjea

    (University of South Florida)

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.

Suggested Citation

  • S. Dhar & A. Mukherjea, 1997. "Convergence in Distribution of Products of I.I.D. Nonnegative Matrices," Journal of Theoretical Probability, Springer, vol. 10(2), pages 375-393, April.
    • Handle: RePEc:spr:jotpro:v:10:y:1997:i:2:d:10.1023_a:1022612516862
    DOI: 10.1023/A:1022612516862
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