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

Author

Listed:
  • A. Mukherjea

    (University of South Florida)

  • J. S. Ratti

    (University of South Florida)

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.

Suggested Citation

  • A. Mukherjea & J. S. Ratti, 1997. "Continuous Singularity of the Weak Limit of Convolution Powers of a Discrete Probability Measure on 2 × 2 Stochastic Matrices," Journal of Theoretical Probability, Springer, vol. 10(2), pages 499-506, April.
    • Handle: RePEc:spr:jotpro:v:10:y:1997:i:2:d:10.1023_a:1022672802749
    DOI: 10.1023/A:1022672802749
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    Cited by:

    1. A. Mukherjea & A. Nakassis & J. S. Ratti, 1999. "On the Distribution of the Limit of Products of I.I.D. 2×2 Random Stochastic Matrices," Journal of Theoretical Probability, Springer, vol. 12(2), pages 571-583, April.

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