Randomized Error of Scrambled Net Quadrature for Tensor Product Sobolev and Korobov Spaces

Scrambled quasi-Monte Carlo quadrature is a hybrid of Monte carlo and quasi-Monte Carlo methods, which combines the best of these two methods for integration. This article studies the performance of the scrambled quadrature rules in randomized settings for the tensor product Sobolev and Korobov spaces of integrands. It is shown that the randomized error of the scrambled （λ, t, ms）-nets is of order n^-3/2log n^（s-1）/2 for these two spaces.