Sufficient conditions for fast quasi-Monte Carlo convergence

AbstractWe study the approximation of d-dimensional integrals. We present sufficient conditions for fast quasi-Monte Carlo convergence. They apply to isotropic and non-isotropic problems and, in particular, to a number of problems in computational finance. We show that the convergence rate of quasi-Monte Carlo is of order n−1+p{logn}−1/2 with p⩾0. This is a worst case result. Compared to the expected rate n−1/2 of Monte Carlo it shows the superiority of quasi-Monte Carlo