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1
Content available remote

The stability of Markov operators on Polish spaces

100%
Szarek T.
Studia Mathematica
|
2000
|
tom 143
|
nr 2
145-152
EN
A sufficient condition for the asymptotic stability of Markov operators acting on measures defined on Polish spaces is presented.
2
Content available remote

Markov operators acting on Polish spaces

100%
Szarek T.
Annales Polonici Mathematici
|
1997
|
tom 67
|
nr 3
247-257
EN
We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.
3
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Generic properties of learning systems

100%
Szarek T.
Annales Polonici Mathematici
|
2000
|
tom 73
|
nr 2
93-103
EN
It is shown that the set of learning systems having a singular stationary distribution is generic in the family of all systems satisfying the average contractivity condition.
4
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Strong and weak stability of some Markov operators

80%
Rudnicki R.
Colloquium Mathematicum
|
2000
|
tom 84/85
|
nr 1
255-263
EN
An integral Markov operator $P$ appearing in biomathematics is investigated. This operator acts on the space of probabilistic Borel measures. Let $μ$ and $ν$ be probabilistic Borel measures. Sufficient conditions for weak and strong convergence of the sequence $(P^{n}μ-P^{n}ν)$ to $0$ are given.
5
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On continuous time version of two-phase cell cycle model of Tyrcha

80%
Zwoleński P.
Mathematica Applicanda
|
2013
|
tom 41
|
nr 1
EN
We consider a model of two-phase cell cycle in a maturity-structured cellular population, which consists of a system of first order linear partial differential equations (transport equations). The model is based on similar biological assumptions as models of Lasota-Mackey, Tyson-Hannsgen and Tyrcha. We examine behavior of the solutions of the system along characteristics, give conditions for existence of invariant density, and compare results with outcomes of generational model.
6
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Random Dynamical Systems with Jumps and with a Function Type Intensity

80%
Kubieniec J.
Annales Mathematicae Silesianae
|
2016
|
tom 30
|
nr 1
63-87
EN
In paper [4] there are considered random dynamical systems with randomly chosen jumps acting on Polish spaces. The intensity of this process is a constant λ. In this paper we formulate criteria for the existence of an invariant measure and asymptotic stability for these systems in the case when λ is not constant but a Lipschitz function.
7
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Markov operators on the space of vector measures; coloured fractals

70%
Baron K., Lasota A.
Annales Polonici Mathematici
|
1998
|
tom 69
|
nr 3
217-234
EN
We consider the family 𝓜 of measures with values in a reflexive Banach space. In 𝓜 we introduce the notion of a Markov operator and using an extension of the Fortet-Mourier norm we show some criteria of the asymptotic stability. Asymptotically stable Markov operators can be used to construct coloured fractals.
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