Paper Title:

On the Convergence in Law of Iterates of Random-Valued Functions

Author(s):

Karol Baron

Uniwersytet Śląski, Instytut Matematyki
 Bankowa 14, PL--40--007 Katowice,
Poland
baron@us.edu.pl

Abstract:

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 * Ω^N by f¹(x,ω) = f(x,ω₁)  and fⁿ⁺¹(x,ω)=f(fⁿ(x,ω),ω_n+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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