Journal of Statistical Physics, VoL 35, Nos. 1/2, 1984, p. 151-158.
We show, by using the Liapunov method, that the Lorenz model perturbed by Gaussian white noise is ergodic for any Rayleigh number. Our theory confirms two properties which have been found by numerical calculation. We also discuss the ergodicity of some other randomly perturbed dissipative systems, a one-dimensional laser, and a homopolar disk dynamo model of the geomagnetism.