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ArticleOriginal scientific text

Title

Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators

Authors 1

Affiliations

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

Abstract

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.

Keywords

ENG
Markov operator, asymptotic stability, residuality, dense Gδ

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Discussiones Mathematicae Probability and Statistics
2012/32/1-2
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Pages:
17-33
Main language of publication
English
Received
2012-04-11
Accepted
2013-02-23
Published
2012

DOI: 10.7151/dmps1141

Exact and natural sciences