  Path integral techniques are used to understand the behaviour of a particle
moving in a bistable potential well and acted upon by quasi-monochromatic
external noise. In the limit of small diffusion coefficient, a steepest descent
evaluation of the path integral enables mean first passage times and the
transition times from one well to the other to be computed. The results and
general approach are compared with computer simulations of the process. It is
found that the bandwidth parameter, $\Gamma$, has a critical value above which
particle escape is by white-noise-like outbursts, but below which escape is by
oscillatory type behaviour.
