Random iteration of one-dimensional transformations
Let S be a measurable space, \(\{f_ s\}_{s\in S}\) a family of transformations from the unit interval into itself, and \(\{X_ n\}^{\infty}_{n=1}\) a sequence of S-valued i.i.d. random variables on a probability space \((\Omega,{\mathcal F},P)\). The author studies the asymptotic behavior of \(x_ n\) where \(x_{n+1}=f_{X_{n+1}(\omega)}(x_ n)\), \(n\geq 0\), \(\omega\in \Omega\). The results generalize those of \textit{S. Tanaka} and \textit{S. Itô} [Tokyo J. Math. 5, 463-478 (1984; Zbl 0528.60065)].
transformations from the unit interval into itself
scientific article; zbMATH DE number 3934146