  Let p:N->M be a surjective map of smooth manifolds. We are concerned with
singular perturbation problems associated to a pair of second order positive
definite differential operators with no zero order terms, that are intertwined
by p. We discuss the associated random perturbations of stochastic differential
equations and present a number of examples including perturbation to geodesic
flows and construction of a Brownian motion on S^2 through homogenisation of
SDE's on the Hopf fibration.
