Stochastic dynamical systems with weak contractivity properties I. Strong and local contractivity

• Autorzy: Marc Peigné , Wolfgang Woess
• Języki publikacji: EN

Abstrakty

EN

Consider a proper metric space 𝖷 and a sequence $(Fₙ)_{n≥0}$ of i.i.d. random continuous mappings 𝖷 → 𝖷. It induces the stochastic dynamical system (SDS) $Xₙ^{x} = Fₙ ∘ ... ∘ F₁(x)$ starting at x ∈ 𝖷. In this and the subsequent paper, we study existence and uniqueness of invariant measures, as well as recurrence and ergodicity of this process.
In the present first part, we elaborate, improve and complete the unpublished work of Martin Benda on local contractivity, which merits publicity and provides an important tool for studying stochastic iterations. We consider the case when the Fₙ are contractions and, in particular, discuss recurrence criteria and their sharpness for the reflected random walk.

Kategorie tematyczne

• 60G50: Sums of independent random variables; random walks
• 60J05: Discrete-time Markov processes on general state spaces
• 37Hxx: Random dynamical systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 125
• Numer: 1
• Strony: 31-54

Daty

wydano

2011

Twórcy

autor

Marc Peigné

• Laboratoire de Mathématiques, et Physique Théorique, Université François Rabelais Tours, Fédération Denis Poisson - CNRS, Parc de Grandmont, 37200 Tours, France

autor

Wolfgang Woess

• Institut für Mathematische Strukturtheorie, (Math C), Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria

Identyfikatory

DOI

10.4064/cm125-1-4