On the asymptotic efficiency of importance sampling techniques

The asymptotic efficiency of importance sampling (IS) techniques for the simulation of rare events in a multidimensional nonlinear setting was studied by J.S. Sadowsky and J.A. Bucklew (see ibid., vol.36, p.579-88, 1990). Fundamental results on the asymptotic efficiency of the mean-value modification (MM) technique were derived. Additionally, a statement was made that other IS techniques cannot be asymptotically efficient. It is shown that for the simulation of digital communication systems with Gaussian input, a broad class of asymptotically efficient IS techniques exists. Necessary and sufficient conditions are provided for the asymptotic efficiency of five different IS techniques (including MM) for one-dimensional linear systems. Multidimensional generalizations of these IS techniques are proposed. A sufficient condition for the asymptotic efficiency of these techniques applied to multidimensional nonlinear systems is provided