Importance sampling for slow-fast diffusions based on moderate deviations

Understand

We consider systems of slow--fast diffusions with small noise in the slow component.

• We construct provably logarithmic asymptotically optimal importance schemes for the estimation of rare events based on the moderate deviations principle.
• Using the subsolution approach we construct schemes and identify conditions under which the schemes will be asymptotically optimal.
• Moderate deviations--based importance sampling offers a viable alternative to large deviations importance sampling when the events are not too rare.