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 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 )).
