Characterization of SRB Measures for Random Dynamical Systems on Banach space

Abstract

This paper considers $C^2$ random dynamical systems on a Banach space, and proves that under some mild conditions, SRB measures are characterized by invariant measures satisfying the Pesin's entropy formula, in which entropy is equal to the sum of positive Lyapunov exponents of the system. This can be regarded as a random version of the main result in Blumenthal and Young's paper \cite{Young17}.Comment: 44pages, revised version with some corrected formulations and argument