A TRANSIENT RANDOM-WALK ON STOCHASTIC MATRICES WITH DIRICHLET DISTRIBUTIONS

• 成果类型: Article
• 署名作者: CHAMAYOU, JF; LETAC, G
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988865
• 发表日期: 1994
• 页码: 424-430
• 关键词: products

摘要

Let X1 be a (d x d) random stochastic matrix such that the rows of X1 are independent, with Dirichlet distributions. The rows of the (d x d) matrix A are the parameters of these Dirichlet distributions, and we assume that the sums of the rows and columns of A provide the same vector r = (r1,...,r(d)). If (X(n))(n=1)infinity are i.i.d., we prove that lim(n-->infinity)(X(n)...X1) almost surely has identical rows, which are Dirichlet distributed with parameter r. Van Assche has proved this for d = 2 and four identical entries for A.