Rare event simulation and splitting for discontinuous random variables (Q2786505)

The authors study the impact of discontinuities in the cdf of a random variable \(X\) by means of three unbiased and corrected estimators. The particularity of the constructed estimators is the fact that they did not require in advance the variable \(X\) to be actually discontinuous or not. Existing studies as declared from the authors did not require the continuity of the cdf of \(X\). This was one first motivation behind the developments in the present paper. The authors studied both the distribution of the number of iterations and the MVUE estimator in the case with strict inequality and the one with non-strict inequality. Efficiency of the theoretical results has been shown also on some numerical examples based on a 2-dimensional diffusive process as well as on the well-known Boolean satisfiability problem.