A note on a theorem of Karlin

✍ Scribed by Örjan Stenflo

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 77 KB
• Volume: 54
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(01)00045-1

✦ Synopsis

We give an example of place-dependent random iterations with two a ne 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 (Paciÿc J. Math. 3 (1953) 725-756).