文章基本信息

标题：Cyclicity and Weak Convergence for Convolution of Measures on Non-negative Matrices
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作者：Santanu Chakraborty ; University of Texas ; Pan American, Edinburg, USA 等
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2007
卷号：69
期号：02
出版社：Indian Statistical Institute
摘要：Let $\mu$ be a probability measure on Borel subsets of $d\times d$ non-negative matrices. Let $S$ be the closed (multiplicative) semigroup generated by the support of $\mu,\, S_{\mu}$. Let the minimal rank of the matrices in $S$ be $2$. Then, we obtain necessary and sufficient conditions for weak convergence of $\mu^{n}$ in terms of cyclicity of $S_{\mu}$ -- a concept first introduced in the work of Chakraborty and Rao (1998, {\it Sankhy\=a A}).
关键词：Convolution sequence, weak convergence, probability measure, semigroups, stochastic matrices, cyclic support