First excursion probabilities of dynamical systems by importance sampling

Based on the Girsanov transformation, this paper develops a method for estimating the first excursion probability of dynamical systems with stationary gauss white noise. The focus is to construct control function that concentrates on the samples paths in the "most important part" of the sample space, to achieve the purpose of variance reduction. The paper uses design point to construct control function. For linear systems, the present approach combines with the time-invariant structure reliability theory to get design points by solving the problem of the optimization. For non-linear systems, the paper uses mirror-images method to get design points. Finally the paper gives two examples. The results show the method of this paper to be correct and effective by comparing with the primitive Monte Carlo method.