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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
Content available remote

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.
3
Content available remote

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
Content available remote

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
Content available remote

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
Content available remote

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.
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
Content available remote

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.
10
Content available remote

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
Content available remote

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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