Quasi-Monte Carlo integration of characteristic functions and the rejection sampling method (Q1961781)

The performance of quasi-Monte Carlo (QMC) integration of indicators (characteristic functions) is improved by replacing the indicator by a continuous function which has the same integral value. This smoothing method is then applied to the rejection sampling method. Next, the rejection method is extended by replacing the acceptance/rejection decision with a sort of `weighted' version. Numerical results illustrated on two integrals (of multiplicity 5 and 7) tend to indicate that importance sampling combined with this extended smoothed rejection method is much more efficient than standard QMC and the unsmoothed rejection method when used with quasi-random numbers.