  We consider a slow passage through a point of loss of stability. If the
passage is sufficiently slow, the dynamics are controlled by additive random
disturbances, even if they are extremely small. We derive expressions for the
`exit value' distribution when the parameter is explicitly a function of time
and the dynamics are controlled by additive Gaussian noise. We derive a new
expression for the small correction introduced if the noise is coloured
(exponentially correlated). There is good agreement with results obtained from
simulation of sample paths of the appropriate stochastic differential
equations. Multiplicative noise does not produce noise-controlled dynamics in
this fashion.
