Variance reduction techniques and quasi-Monte Carlo methods

Quasi-Monte Carlo methods can be described as deterministic versions of Monte Carlo methods. Variance reduction techniques are widely used for improving the efficiency of Monte Carlo methods. In this paper, we study the possibility of using the deterministic versions of some variance reduction techniques for the variation reduction in the context of quasi-Monte Carlo methods. We combine the flexibility of Monte Carlo methods with the effectiveness and fast convergence of quasi-Monte Carlo methods. Quasi-random integration rules that integrate exactly some class of functions are constructed.