Large fluctuations and fluctuational transitions in systems driven by colored Gaussian noise: A high-frequency noise

Abstract

The quasistationary distribution and the transition probabilities for systems driven by weak noise are analyzed to logarithmic accuracy. The problem is reduced to the boundary-value problem for the set of ordinary differential equations. The form of the equations is determined by the shape of the power spectrum of noise. They are solved in the limiting cases of small and large times characterizing noise correlations, and also for a high-frequency narrow-band noise. The dependences of the logarithm of the distribution on the parameters and the coordinate of the system are quite specific in the latter case. The logarithms of the transition probability and of the quasistationary distribution in the point separating the ranges of attraction to different stable states differ from each other.