Displaying similar documents to “Invariant measures for position dependent random maps with continuous random parameters”

Position dependent random maps in one and higher dimensions

Wael Bahsoun, Paweł Góra (2005)

Studia Mathematica

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A random map is a discrete-time dynamical system in which one of a number of transformations is randomly selected and applied on each iteration of the process. We study random maps with position dependent probabilities on the interval and on a bounded domain of ℝⁿ. Sufficient conditions for the existence of an absolutely continuous invariant measure for a random map with position dependent probabilities on the interval and on a bounded domain of ℝⁿ are the main results.

On gradient-like random dynamical systems

Aya Hmissi, Farida Hmissi, Mohamed Hmissi (2012)

ESAIM: Proceedings

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This paper deals with some characterizations of gradient-like continuous random dynamical systems (RDS). More precisely, we establish an equivalence with the existence of random continuous section or with the existence of continuous and strict Liapunov function. However and contrary to the deterministic case, parallelizable RDS appear as a particular case of gradient-like RDS. The obtained results are generalizations of well-known analogous theorems in the framework of deterministic...

A note on correlation coefficient between random events

Czesław Stępniak (2015)

Discussiones Mathematicae Probability and Statistics

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Correlation coefficient is a well known measure of (linear) dependence between random variables. In his textbook published in 1980 L.T. Kubik introduced an analogue of such measure for random events A and B and studied its basic properties. We reveal that this measure reduces to the usual correlation coefficient between the indicator functions of A and B. In consequence the resuts by Kubik are obtained and strenghted directly. This is essential because the textbook is recommended by...

Strong Unique Ergodicity of Random Dynamical Systems on Polish Spaces

Paweł Płonka (2016)

Annales Mathematicae Silesianae

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In this paper we want to show the existence of a form of asymptotic stability of random dynamical systems in the sense of L. Arnold using arguments analogous to those presented by T. Szarek in [6], that is showing it using conditions generalizing the notion of tightness of measures. In order to do that we use tightness theory for random measures as developed by H. Crauel in [2].