Variance reduction by means of deterministic computation: Collision estimate (Q1973293)

The paper studies the collision estimate of Monte Carlo methods for the solution of integral equations. A new variant of a variance reduction technique is proposed and analyzed. The paper modifies the classical Monte Carlo algorithm, the absorption scheme, developed in a recent paper of the author [Monte Carlo Methods Appl. 1, No. 4, 251-277 (1995; Zbl 0843.65096)] and uses instead the collision scheme technique. After presenting the new technique for the collision scheme it is shown that the variance is dominated by the square of the proximity of the respective kernels and right-hand sides in some functions space norms. The results of the author [loc. cit.] can then be carried over to the collision scheme, such as the Galerkin method to construct a neighbouring equation and the estimation of proximity of kernels as well as right-hand sides from certain parameters of that method.