Convergence of sequences of iterates of random-valued vector functions

• Autorzy: Rafał Kapica
• Języki publikacji: EN

Abstrakty

EN

Given a probability space (Ω,𝓐, 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,·)).

Kategorie tematyczne

• 60F25: L p -limit theorems
• 37H99: None of the above, but in this section
• 60F15: Strong theorems
• 39B12: Iteration theory, iterative and composite equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 97
• Numer: 1
• Strony: 1-6

Daty

wydano

2003

Twórcy

autor

Rafał Kapica

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Identyfikatory

DOI

10.4064/cm97-1-1