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Paper Title:
On
the Convergence in Law of Iterates of Random-Valued Functions
Author(s):
Karol Baron
Uniwersytet
Śląski, Instytut MatematykiAbstract:
Given a probability space (Ω,
A, P) a separable and complete metric space X with the
σ-algebra B of all
its Borel subsets and a B
A -measurable f : X
*
Ω
→ X we consider its iterates fn, n
N,
defined on X
*
ΩN by f1(x,ω) = f(x,ω1) and
fn+1(x,ω)=f(fn(x,ω),ωn+1),
provide a simple criterion for the convergence in law of
fn(x,·))
n
N, to a random variable independent of
x
X , and apply
this criterion to linear functional equations in a single variable.
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