On Stable Oscillations and Equilibriums Induced by Small Noise

摘要

We consider the motion of a light particle when the force field is perturbed by a 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 calculate the correction term which appears when the Gaussian perturbations are replaced by the simple random walk. These are the stochastic-resonance-type effects, and their mathematical description is based on the large deviation theory.