On asymptotically efficient simulation of large deviation probabilities

Let $\{\nu_{\varepsilon}, \varepsilon >0\}$ be a family of probabilities for which the decay is governed by a large deviation principle, and consider the simulation of $\nu_{\varepsilon_0}(A)$ for some fixed measurable set $A$ and some $\varepsilon_0>0.$ We investigate the circumstances under which an exponentially twisted importance sampling distribution yields an asymptotically efficient estimator. Varadhan's lemma yields necessary and sufficient conditions, and these are shown to improve on certain conditions of Sadowsky. This is illustrated by an example to which Sadowsky's conditions do not apply, yet for which an efficient twist exists.