On stable oscillations and equilibriums induced by small noise

We consider the motion of a light particle when the force field is perturbe d by ii small nose. If a certain relation between the mass of the particle and the noise intensity holds, the motion of the particle will be close to periodic oscillations or to a stable equilibrium which do not exist without the noise. We study various classes of random perturbations. In particular , we consider the question of computer simulation of these effects and calc ulate the correction term which appears when the Gaussian perturbations are replaced by the simple random walk. These are the stochastic-resonance-typ e effects, and their mathematical description is based on the large deviati on theory.