  In this paper we analyze a chemostat model with wall growth where the input
flow is affected by two different stochastic processes: the well-known standard
Wiener process, which leads into several drawbacks from the biological point of
view, and a suitable Orsntein-Uhlenbeck process depending on some parameters
which allow us to control the noise to be bounded inside some interval that can
be fixed previously by practitioners. Thanks to this last approach, which has
already proved to be very realistic when modeling other simplest chemostat
models, it will be possible to prove the persistence and coexistence of the
species in the model without needing the theory of random dynamical systems and
pullback attractors needed when dealing with the Wiener process which,
moreover, does not provide much information about the long-time behavior of the
systems in many situations.
