Optimal input potential functions in the interacting particle system method
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The assessment of the probability of a rare event with a naive Monte-Carlo method is computationally intensive, so faster estimation methods, such as variance reduction methods, are needed. We focus on one of these methods which is the interacting particle (IPS) system method. The method requires to specify a set of potential functions. The choice of these functions is crucial, because it determines the magnitude of the variance reduction. So far, little information was available on how to choose the potential functions. To remedy this, we provide the expression of the optimal potential functions minimizing the asymptotic variance of the estimator of the IPS method.
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