Fast convergence of quasi-Monte Carlo for a class of isotropic integrals

We consider the approximation of d-dimensional weighted integrals of certai n isotropic functions. We are mainly interested ill cases where d is large. We show that the convergence rate of quasi-Monte Carlo for the approximati on of these integrals is O(root logn/n). Since this is a worst case result, compared to the expected convergence rate O(n(-1/2)) of Monte Carlo, it sh ows the superiority of quasi-Monte Carlo for this type of integral. This is much faster than the worst case convergence, O(log(d) n/n), of quasi-Monte . Carlo.