RANDOMLY CONNECTED DYNAMICAL SYSTEMS ON BANACH SPACES

Abstract

We give sufficient conditions for asymptotic stability of Markov operators governing the evolution of measures due to the action of randomly chosen dynamical systems on Banach spaces. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for a semigroup generated by the considered systems.

Keywords:

• Dynamical systems
• Markov operator
• Asymptotic stability

Acknowledgments