Escape from a fluctuating double well

We study thermally driven escape from a double well over a fluctuating barrier height. The fluctuations of the bistable potential are governed by exponentially correlated Gaussian noise of weak-to-moderate-to-large noise correlation time {τ}. Exact results are obtained for the limiting cases of very fast ({τ}{→}0) and very slow ({τ}{→}{∞}) barrier fluctuations. For finite noise color {τ}, we present approximation schemes for the stochastic dynamics of nonlinear systems that are driven simultaneously by both a white noise source and a multiplicative colored noise (colored noise driven parametric stochastic flows). Our approximative results for arbitrary, but finite noise color {τ} become exact for escape in a piecewise parabolic bistable potential with a cusp at the transition state.