Effective branching splitting method under cost constraint

This paper deals with the splitting method first introduced in rare event analysis. In this technique, the sample paths are split into R multiple copies at various stages during the simulation. Given the cost, the optimization of the algorithm suggests sampling a number of subtrials which may be non-integer and even unknown but estimated. To avoid this problem, we present in this paper three different approaches which provide precise estimates of the relative error between and its estimator.