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We consider the general problem of the simulation of highly reliable systems operating in the presence of Gaussian noise. Our methodology uses importance sampling which has been shown to be a particularly effective method in the general discipline of rare-event simulation. The methods we propose are optimal in a certain sense, i.e., they are efficient. We also give a new class of simulation distributions that are universally efficient in the sense that they depend only on a single scalar parameter, regardless of the dimensionality of the underlying system or of the error sets to be simulated.
Date of Publication: Feb 2003