Convergence of sequences of iterates of random-valued vector functions

Rafał Kapica. "Convergence of sequences of iterates of random-valued vector functions." Colloquium Mathematicae 97.1 (2003): 1-6. <http://eudml.org/doc/284397>.

@article{RafałKapica2003,
abstract = {Given a probability space (Ω,, P) and a closed subset X of a Banach lattice, we consider functions f: X × Ω → X and their iterates $fⁿ: X × Ω^\{ℕ\} → X$ defined by f¹(x,ω) = f(x,ω₁), $f^\{n+1\}(x,ω) = f(fⁿ(x,ω),ω_\{n+1\})$, and obtain theorems on the convergence (a.s. and in L¹) of the sequence (fⁿ(x,·)).},
author = {Rafał Kapica},
journal = {Colloquium Mathematicae},
keywords = {iteration theory; limit theorems; probability space; Banach lattice; fixed point; convergence},
language = {eng},
number = {1},
pages = {1-6},
title = {Convergence of sequences of iterates of random-valued vector functions},
url = {http://eudml.org/doc/284397},
volume = {97},
year = {2003},
}

TY - JOUR
AU - Rafał Kapica
TI - Convergence of sequences of iterates of random-valued vector functions
JO - Colloquium Mathematicae
PY - 2003
VL - 97
IS - 1
SP - 1
EP - 6
AB - Given a probability space (Ω,, P) and a closed subset X of a Banach lattice, we consider functions f: X × Ω → X and their iterates $fⁿ: X × Ω^{ℕ} → X$ defined by f¹(x,ω) = f(x,ω₁), $f^{n+1}(x,ω) = f(fⁿ(x,ω),ω_{n+1})$, and obtain theorems on the convergence (a.s. and in L¹) of the sequence (fⁿ(x,·)).
LA - eng
KW - iteration theory; limit theorems; probability space; Banach lattice; fixed point; convergence
UR - http://eudml.org/doc/284397
ER -