文章基本信息

标题：Convergence of Convolution Powers of a Probability Measure on $d\times d$ Stochastic Matrices and a Cyclicity Condition
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作者：Edgardo Cureg ; University of South Florida ; USA Arunava Mukherjea 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：This paper is concerned with a very interesting cyclicity condition introduced by Chakraborty and Rao (1998). The results show that if $\mu$ is a probability measure on $3\times 3$ stochastic matrices, and the minimal rank $r$ of the matrices in the closed semigroup $S$ generated by $S_\mu,$ the support of $\mu,$ is $2,$ then the sequence $(\mu^n)$ of convolution powers of $\mu$ does {\em not} converge weakly if and only if $S_\mu$ is cyclic. Here we extend this result to any $d>3.$ Moreover, we show that when the minimal rank $r$ above is not $2,$ this result does not always hold.
关键词：Convolution sequence, weak convergence, probability measure, semigroups, stochastic matrices, cyclic support.