state-dependent importance sampling and large deviations
Large deviations analysis for light-tailed systems provides an asymptotic description of the optimal importance sampler in the scaling of the Law of Large Numbers. As we will show by means of a simple example related to computational finance, such asymptotic description can be interpreted indifferent ways suggesting several importance sampling algorithms, some of them state-dependent. In turn, the performance of the suggested algorithms can be substantially different.
importance sampling large deviations random walks rare-event simulation