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1
Content available remote

Exponential Convergence For Markov Systems

100
Ślęczka M.
Annales Mathematicae Silesianae
|
2015
|
tom 29
|
nr 1
139-149
EN
Markov operators arising from graph directed constructions of iterated function systems are considered. Exponential convergence to an invariant measure is proved.
2
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Stability of Markov processes nonhomogeneous in time

80
Tyran-Kamińska M.
Annales Polonici Mathematici
|
1999
|
tom 71
|
nr 1
47-59
EN
We study the asymptotic behaviour of discrete time processes which are products of time dependent transformations defined on a complete metric space. Our sufficient condition is applied to products of Markov operators corresponding to stochastically perturbed dynamical systems and
fractals.
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3
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Invariant measures for iterated function systems

80
Szarek T.
Annales Polonici Mathematici
|
2000
|
tom 75
|
nr 1
87-98
EN
A new criterion for the existence of an invariant distribution for Markov operators is presented. Moreover, it is also shown that the unique invariant distribution of an iterated function system is singular with respect to the Hausdorff measure.
4
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Dynamical systems with multiplicative perturbations: the strong convergence of measures

80
Horbacz K.
Annales Polonici Mathematici
|
1993
|
tom 58
|
nr 1
85-93
EN
We give sufficient conditions for the strong asymptotic stability of the distributions of dynamical systems with multiplicative perturbations. We apply our results to iterated function systems.
5
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On the strong convergence to equilibrium of the Foiaş solutions of the transport equation

80
Malczak J.
Annales Polonici Mathematici
|
1992
|
tom 57
|
nr 2
193-203
EN
We define the Foiaş solutions of the transport equation and we prove that the strong asymptotic stability of the Foiaş solutions is equivalent to the asymptotic stability of the solutions of the transport equation in L¹.
6
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Krengel-Lin decomposition for noncompact groups

80
Bartoszek W., Rębowski R.
Colloquium Mathematicum
|
1996
|
tom 69
|
nr 1
87-94
7
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Asymptotic behaviour in the set of nonhomogeneous chains of stochastic operators

80
Pułka M.
Discussiones Mathematicae Probability and Statistics
|
2012
|
tom 32
|
nr 1-2
17-33
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.
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8
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On a nonstandard approach to invariant measures for Markov operators

80
Wiśnicki A.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2010
|
tom 64
|
nr 2
EN
We show the existence of invariant measures for Markov-Feller operators defined on completely regular topological spaces which satisfy the classical positivity condition.
9
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Randomly connected dynamical systems - asymptotic stability

80
Horbacz K.
Annales Polonici Mathematici
|
1998
|
tom 68
|
nr 1
31-50
EN
We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure
for the semigroup generated by the system.
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10
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Markov operators: applications to diffusion processes and population dynamics

80
Rudnicki R.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 1
67-79
EN
This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.
11
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Asymptotic properties of Markov operators defined by Volterra type integrals

70
Baron K., Lasota A.
Annales Polonici Mathematici
|
1993
|
tom 58
|
nr 2
161-175
EN
New sufficient conditions for asymptotic stability of Markov operators are given. These criteria are applied to a class of Volterra type integral operators with advanced argument.
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