  The full family of discrete logistic maps has been widely studied both as a
canonical example of the period-doubling route to chaos, and as a model of
natural processes. In this paper we present a study of the stochastic process
described by iterations of the logistic map with a random parameter. In
addition to bringing together previously known results, we present a proof that
the unique invariant measure of the process in the chaotic regime is
asymptotically stable.
