On the nonuniqueness of the invariant probability for i.i.d. random logistic maps
成果类型：
Article
署名作者：
Athreya, KB; Dai, JJ
署名单位：
Iowa State University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2002
页码：
437-442
关键词：
摘要：
Let {X-n}(0)(infinity) be a Markov chain with values in [0, 1] generated by the iteration of random logistic maps defined by Xn+1 = f(Cn+1) (X-n) equivalent to Cn+1 X-n (1 - X-n), n = 0, 1, 2,..., with {C-n}(1)(infinity) being independent and identically distributed random variables with values in [0, 4] and independent of X-0. This paper provides a class of examples where C-i take only two values lambda and mu such that there exist two distinct invariant probability distributions pi(0) and pi(1) supported by the open interval (0, 1). This settles a question raised by R. N. Bhattacharya.