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Cyclicity and Weak Convergence for Convolution of Measures on Non-negative Matrices

Santanu Chakraborty
Sankhyā: The Indian Journal of Statistics (2003-2007)
Vol. 69, No. 2 (MAY 2007), pp. 304-313
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25664557
Page Count: 10
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Cyclicity and Weak Convergence for Convolution of Measures on Non-negative Matrices
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Abstract

Let μ be a probability measure on Borel subsets of d × d non-negative matrices. Let S be the closed (multiplicative) semigroup generated by the support of μ, Sμ. Let the minimal rank of the matrices in S be 2. Then, we obtain necessary and sufficient conditions for weak convergence of μn in terms of cyclicity of Sμ — a concept first introduced in the work of Chakraborty and Rao (1998, Sankhyā A).

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