ИСТИНА

Monte Carlo integration typically has an error variance of the form 𝜎2/𝑛, where 𝑛 is a sample size. We can make the variance smaller by using a larger value of 𝑛, but the cost of the corresponding estimate also grows with 𝑛. Therefore it is important to find a way to reduce 𝜎 instead of increasing the sample size 𝑛. To this end, one can try to construct a new Monte Carlo problem with the same expectation as our the original one but with a lower variance 𝜎. We are going to discuss an approach which is based on minimization of the empirical variance over a suitable class of zero mean control functionals. We present the corresponding convergence analysis and a simulation study showing numerical efficiency of the proposed approach.