Noise-induced escape rate over a potential barrier: Results for general noise

We extend a recent instanton calculation of the escape rate over a one-dimensional potential barrier in the weak-noise limit (D0), from the case where the noise is Gaussian and exponentially correlated to a more general process. Specifically, the system we initially consider consists of a Langevin equation x-V(x)+, where is a Gaussian noise with zero mean and correlator (t)(t)=(D)C(t-t) being the noise correlation time. Using a path-integral formulation of this process, we find that, in the weak-noise limit, exp(-S/D) and calculate S order 6 for an arbitrary double-well potential. The extension to non-Gaussian processes is briefly discussed. © 1989 The American Physical Society.