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On the Continuous Singularity of the Limit Distribution of Products of I.I.D. d×d Stochastic Matrices

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Abstract

This article gives sufficient conditions for the limit distribution of products of i.i.d. d×d random stochastic matrices, d finite and ≥2, to be continuous singular, when the support of the distribution of the individual random matrices is finite or countably infinite. Proofs are based on applications of the multivariate Central Limit Theorem.

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Authors and Affiliations

  1. Department of Mathematics, University of South Florida, Tampa, Florida, 33620-5700

    A. Mukherjea

  2. National Institute of Standards & Technology, Gaithersburg, Maryland, 20899

    A. Nakassis

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  1. A. Mukherjea
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  2. A. Nakassis
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Correspondence to A. Mukherjea.

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Mukherjea, A., Nakassis, A. On the Continuous Singularity of the Limit Distribution of Products of I.I.D. d×d Stochastic Matrices. Journal of Theoretical Probability 15, 903–918 (2002). https://doi.org/10.1023/A:1020636603528

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  • DOI: https://doi.org/10.1023/A:1020636603528

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