Monte Carlo complexity of parametric integration
This article is an application of Monte Carlo methods to perform multivariate integration. Usually, Monte Carlo methods are used to approximate single integrals. Goal of this article is to study the case of parametric integration, that is cases where the integrad depends on a parameter. An open research field is the complexity analysis of parametric integration. This paper consider the complexity of computing integrals depending on a parameter for smooth integrands. An optimal algorithm is developed on the basis of a multigrid variance reduction technique. The complexity analysis implies that the algorithm attains a higher convergence rate than any deterministic algorithm. Because of savings due to computation on multiple grids, this rate is also higher than that of previously developed Monte Carlo algorithms for parametrics integration.
scientific article; zbMATH DE number 1389252