A note on a theorem of Karlin

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• 作者：Stenflo ; Ö ; rjan
• 关键词：28D05 ; 28A80 ; 37H99 ; 60J05 ; 60G10 ; Iterated Function Systems (IFS) ; Random systems with complete connections ; Markov chains ; Invariant measures ; Stationary measures ; g-measures
• 刊名：Statistics and Probability Letters
• 出版年：2001
• 出版时间：September 15, 2001
• 年：2001
• 卷：54
• 期：2
• 页码：183-187
• 全文大小：77.0 K

文摘

We give an example of place-dependent random iterations with two affine contractions on the unit interval generating a Markov chain with more than one stationary probability measure. The probability function is continuous and strictly positive. This constitutes a counterexample to a conjecture raised by an incomplete proof by Karlin (Pacific J. Math. 3 (1953) 725–756).