A comparison of RESTART implementations

The RESTART method is a widely applicable simulation technique for the estimation of rare event probabilities. The method is based on the idea to restart the simulation in certain system states, in order to generate more occurrences of the rare event. One of the main questions for any RESTART implementation is how and when to restart the simulation, in order to achieve the most accurate results for a fixed simulation effort. We investigate and compare, both theoretically and empirically, different implementations of the RESTART method. We find that the original RESTART implementation, in which each path is split into a fixed number of copies, may not be the most efficient one. It is generally better to fix the total simulation effort for each stage of the simulation. Furthermore, given this effort, the best strategy is to restart an equal number of times from each state, rather than to restart each time from a randomly chosen stat

Towards zero variance estimators for rare event probabilities

Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events E_{n}:=(f(X_{1})+...+f(X_{n}))\inA_{n} where the summands are i.i.d. and E_{n} is a large or moderate deviation event. The approximation of the conditional density of the real r.v's X_{i} 's, for 1\leqi\leqk_{n} with repect to E_{n} on long runs, when k_{n}/n\to1, is handled. The maximal value of k compatible with a given accuracy is discussed; algorithms and simulated results are presented