Language:
EN
| Published:
29-10-2024
|
Abstract
| pp. 76-93
A transfunction is a function which maps between sets of finite measures on measurable spaces. In this paper we characterize transfunctions that correspond to Markov operators and to plans; such a transfunction will contain the “instructions” common to several Markov operators and plans. We also define the adjoint of transfunctions in two settings and provide conditions for existence of adjoints. Finally, we develop approximations of identity in each setting and use them to approximate weakly-continuous transfunctions with simple transfunctions; one of these results can be applied to some optimal transport problems to approximate the optimal cost with simple Markov transfunctions.
Language:
EN
| Published:
30-09-1993
|
Abstract
| pp. 99-108
We consider discret time dynamical systems with multiplicative perturbations. We give a sufficient condition for the asymptotic stability of Markov operators on measures generated by dynamical systems with multiplicative perturbations.
Language:
EN
| Published:
30-09-2015
|
Abstract
| pp. 139-149
Markov operators arising from graph directed constructions of iterated function systems are considered. Exponential convergence to an invariant measure is proved.
We use the approach from Czudek and Szarek (see [1]) to prove the central limit theorem for a stationary Markov chain generated by an iterative function system for a family of increasing, injective functions on [0, 1] with "contractive" properties. We introduce a new approach to prove existence of an unique invariant measure using e-property (see [2]).
Language:
EN
| Published:
15-07-2024
|
Abstract
| pp. 134-154
The paper below is a written version of the 17th Andrzej Lasota Lecture presented on January 12th, 2024 in Katowice. During the lecture we tried to show the impact of Andrzej Lasota’s results on the author’s research concerning various fields of mathematics, including chaos and ergodicity of dynamical systems, Markov operators and semigroups and partial differentia equations.
2024-07-15
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English