2012 , Volume 17, № 2, p.99-114

Applications of Monte Carlo methods to the problems of particles transport are considered. Issues related to the reduction of algorithms cost, using estimators choice, are analysed. For the computing the averages over given surfaces and volumes there are well known imitation estimators such as collisions, track lengths, and surface intersections estimators. The expected value estimators are well known too. All of them correspond to the special approximations to solutions of adjoint problems φ. In the present paper, non-imitation estimators from "zero"class are constructed in which the approximations φ, are close to above named estimators approximations in some domains. Variances of these non-imitation estimators are close to variances of the expected value estimators while the former ones are less computationally expensive.. Theoretical constructions and hypotheses are confirmed by numerical experiments, in particular, experiments on space distributions of particles. The paper concentrates on the cases of cylindrical and plane rings surfaces, and on cylindrical volumes.