Armen Shirikyan Ergodicty for a class of Markov processes and applications to randomly forced PDE's. I (195K, Postscript) ABSTRACT. The paper is devoted to studying the problem of ergodicity for dissipative PDE's perturbed by an external random force. We give a simple sufficient condition for uniqueness and stability of a stationary measure for a family of Markov processes. The result obtained is applied to the 2D NS system.