Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators

• Autorzy: Małgorzata Pułka
• Języki publikacji: EN

Abstrakty

EN

We study different types of asymptotic behaviour in the set of (infinite dimensional) nonhomogeneous chains of stochastic operators acting on L¹(μ) spaces. In order to examine its structure we consider different norm and strong operator topologies. To describe the nature of the set of nonhomogeneous chains of Markov operators with a particular limit behaviour we use the category theorem of Baire. We show that the geometric structure of the set of those stochastic operators which have asymptotically stationary density differs depending on the considered topologies.

Słowa kluczowe

EN

Markov operator; asymptotic stability; residuality; dense $G_{δ}$

Kategorie tematyczne

• 54H20: Topological dynamics
• 47A35: Ergodic theory
• 47B65: Positive operators and order-bounded operators
• 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2012
• Tom: 32
• Numer: 1-2
• Strony: 17-33

Daty

wydano

2012

otrzymano

2012-04-11

poprawiono

2013-02-23

Twórcy

autor

Małgorzata Pułka

• Department of Mathematics, Gdańsk University of Technology, ul. Gabriela Narutowicza 11/12, 80-233, Gdańsk, Poland

Bibliografia

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Identyfikatory

DOI

10.7151/dmps1141