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 RR 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 P(A)P(A) and its estimator.