On the convergence of sequences of iterates of random-valued vector functions

Volume 90 / 2007

Rafa/l Kapica Annales Polonici Mathematici 90 (2007), 193-201 MSC: Primary 39B12; Secondary 37H99, 60F15. DOI: 10.4064/ap90-3-1


Given a probability space $({\mit \Omega },{{\mathcal A}},P)$ and a subset $X$ of a normed space we consider functions $f:X\times {\mit \Omega }\to X$ and investigate the speed of convergence of the sequence $(f^n(x,\cdot ))$ of the iterates $f^n:X\times {\mit \Omega }^{{\mathbb N}}\to X$ defined by $f^1(x,\omega )=f(x,\omega _1)$, $f^{n+1}(x,\omega )=f(f^n(x,\omega ),\omega _{n+1})$.


  • Rafa/l KapicaInstitute of Mathematics
    Silesian University
    Bankowa 14
    40-007 Katowice, Poland

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