In some settings the deliberate introduction of noise can have a beneficial effect on the rate of convergence of numerical algorithms for finding the minima of functions. This is an important aspect of simulated annealing. However, there are situations which, in contrast to simulated annealing, do not involve reducing the noise level with time and which are also of interest in a computational and control context. Problems of this type are considered. The effect of the addition of a noise term to the solution of a differential equation is investigated via properties of the associated Fokker-Plank operator. >