  The authors consider stochastic aspects of the stabilization problem for two
and three-dimensional Oseen equations with help of feedback control defined on
a part of the fluid boundary. Stochastic issues arise when inevitable
unpredictable fluctuations in numerical realization of stabilization procedures
are taken into account and they are supposed to be independent identically
distributed random variables. Under this assumption the solution to the
stabilization problem obtained via boundary feedback control can be described
by a Markov chain or a discrete random dynamical system. It is shown that this
random dynamical system possesses a unique, exponentially attracting, invariant
measure, namely, this random dynamical system is ergodic. This gives adequate
statistical description of the stabilization process on the stage when
stabilized solution has to be retained near zero (i.e. near unstable state of
equilibrium).
