# Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators

Discussiones Mathematicae Probability and Statistics (2012)

- Volume: 32, Issue: 1-2, page 17-33
- ISSN: 1509-9423

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topMałgorzata Pułka. "Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators." Discussiones Mathematicae Probability and Statistics 32.1-2 (2012): 17-33. <http://eudml.org/doc/270869>.

@article{MałgorzataPułka2012,

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.},

author = {Małgorzata Pułka},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {Markov operator; asymptotic stability; residuality; dense $G_\{δ\}$; denseness},

language = {eng},

number = {1-2},

pages = {17-33},

title = {Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators},

url = {http://eudml.org/doc/270869},

volume = {32},

year = {2012},

}

TY - JOUR

AU - Małgorzata Pułka

TI - Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators

JO - Discussiones Mathematicae Probability and Statistics

PY - 2012

VL - 32

IS - 1-2

SP - 17

EP - 33

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/270869

ER -

## References

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