科研之友
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摘要
Problems similar to Ann. Prob. 22 (1994) 424-430 and J. Appl. Prob. 23 (1986) 1019-1024 are considered here. The limit distribution of the sequence X (n) X (n-1)a <-X (1), where (X (n) ) (n a parts per thousand yen 1) is a sequence of i.i.d. 2 x 2 stochastic matrices with each X (n) distributed as mu, is identified here in a number of discrete situations. A general method is presented and it covers the cases when the random components C (n) and D (n) (not necessarily independent), (C (n) , D (n) ) being the first column of X (n) , have the same (or different) Bernoulli distributions. Thus (C (n) , D (n) ) is valued in {0, r}(2), where r is a positive real number. If for a given positive real r, with , r (-1) C (n) and r (-1) D (n) are each Bernoulli with parameters p (1) and p (2) respectively, 0 < p (1), p (2)< 1 (which means and ), then it is well known that the weak limit lambda of the sequence mu (n) exists whose support is contained in the set of all 2 x 2 rank one stochastic matrices. We show that S(lambda), the support of lambda, consists of the end points of a countable number of disjoint open intervals and we have calculated the lambda-measure of each such point. To the best of our knowledge, these results are new.
- 出版日期2014-11
