Rare event simulation for rough energy landscapes

A rough energy landscape can be modeled by a potential function superimposed by another fast oscillating function. Modeling motion in such a rough energy landscape by a small noise stochastic differential equation with fast oscillating coefficients, we construct asymptotically optimal importance sampling schemes for the study of rare events. Standard Monte Carlo methods perform poorly for these kind of problems in the small noise limit, even without the added difficulties of the fast oscillating function. We study the situation in which the fast oscillating parameter goes to zero faster than the intensity of the noise. We identify an asymptotically optimal estimator in the sense of variance minimization using the subsolution approach. Examples and simulation results are provided.