On iterates of strong Feller operators on ordered phase spaces

• Autorzy: Wojciech Bartoszek
• Języki publikacji: EN

Abstrakty

EN

Let (X,d) be a metric space where all closed balls are compact, with a fixed σ-finite Borel measure μ. Assume further that X is endowed with a linear order ⪯. Given a Markov (regular) operator P: L¹(μ) → L¹(μ) we discuss the asymptotic behaviour of the iterates Pⁿ. The paper deals with operators P which are Feller and such that the μ-absolutely continuous parts of the transition probabilities ${P(x,·)}_{x∈X}$ are continuous with respect to x. Under some concentration assumptions on the asymptotic transition probabilities $P^{m}(y,·)$, which also satisfy inf(supp Pf₁) ⪯ inf(supp Pf₂) whenever inf(supp f₁) ⪯ inf(supp f₂), we prove that the iterates Pⁿ converge in the weak* operator topology.

Kategorie tematyczne

• 60J35: Transition functions, generators and resolvents
• 62P10: Applications to biology and medical sciences
• 47A35: Ergodic theory
• 37A30: Ergodic theorems, spectral theory, Markov operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 101
• Numer: 1
• Strony: 121-134

Daty

wydano

2004

Twórcy

autor

Wojciech Bartoszek

• Department of Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/cm101-1-8