An analysis of the LRE-Algorithm using Sojourn times

The classical method of evaluation of simulations surely is the batch means method, see e.g. [Bratley et al. 1987], giving confidence intervals to express the precision of the simulation results. Unfortunately, it is not suited for rare event simulation techniques, as they do not produce the necessary large batches. As an alternative, the LRE-algorithm has been introduced in [Schreiber 1984], where the lengthy final analysis of its basis has just been given in [Schreiber 1999]. Its name is based on the ‘Limited Relative Error’ that has been chosen to describe the precision of the results. In this paper, we present another, much simpler, analysis of the LRE-algorithm based on sojourn times, which gives a better understanding of the algorithm and clearly exhibits certain limitations. Additionally, it allows to create confidence intervals, and so it is possible to compare the results of the two very different methods.