Sufficient conditions for fast quasi-Monte Carlo convergence

We 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{log n}-1/2) with p greater than or equal to 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. (C) 2002 Elsevier Science (USA). All rights reserved.