  Consider a piecewise smooth expanding map of the interval possessing several
invariant subintervals and the same number of ergodic absolutely continuous
invariant probability measures (ACIMs). After this system is perturbed to make
the subintervals lose their invariance in such a way that there is a unique
ACIM, we show how to approximate the diffusion coefficient for an observable of
bounded variation by the diffusion coefficient of a related continuous time
Markov chain.
