Efficient simulation of large deviation events for sums of random vectors using saddle-point representations (Q2854076)

This paper focuses on the rare event problem of efficient estimation of the density function of the average of i.i.d. light-tailed random vectors evaluated away from their mean, and the tail probability that this average takes a large deviation. In a single-dimension setting it considers the estimation problem of the expected overshoot associated with a sum of i.i.d. random variables taking large deviations. The saddle-point representation for the performance measures is used and importance sampling is applied to develop probably efficient unbiased estimation algorithms.NEWLINENEWLINEThe key contribution of the paper is combining the rare event simulation with the classical theory of saddle-point-based approximations for tail events. Two numerical experiments are shown: the estimation of the probability density function and the estimation of the tail probability. The experiments compare the presented method with the conditional Monte Carlo method and the optimal state-dependent exponential twisting method, respectively. It is shown that the proposed algorithm provides an estimator with much smaller variance in both cases.