  This paper considers $C^2$ random dynamical systems in a Banach space, and
proves that under some mild conditions, SRB measures are characterized by
invariant measures satisfying 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}.
