Convergence of sequences of iterates of random-valued vector functions
Volume 97 / 2003
Colloquium Mathematicum 97 (2003), 1-6
MSC: Primary 39B12; Secondary 37H99, 60F15, 60F25.
DOI: 10.4064/cm97-1-1
Abstract
Given a probability space $({\mit \Omega },{{\mathcal A}},P)$ and a closed subset $X$ of a Banach lattice, we consider functions $f:X\times {\mit \Omega }\to X$ and their iterates $f^n:X\times {\mit \Omega }^{{{\mathbb N}}}\to X$ defined by $f^1(x,\omega )=f(x,\omega _1)$, $f^{n+1}(x,\omega )=f(f^n(x,\omega ),\omega _{n+1})$, and obtain theorems on the convergence (a.s. and in $L^1$) of the sequence $(f^n(x,\cdot ))$.
