On Koopman and Perron-Frobenius operators of random dynamical systems

Abstract

In this paper, we investigate the Koopman and the Perron-Frobenius operators of random dynamical systems in general setting. Moreover, we give some necessary and sufficient conditions for the existence of invariant densities for the associated Perron-Frobenius operators.

Keywords

• dynamical system
• random dynamical system
• factorization
• random equation
• koopman operator
• perron-frobenius operator
• invariant measure
• invariant density