Quasi-Monte Carlo methods for simulation

Quasi-Monte Carlo (QMC) methods are numerical techniques for estimating large-dimensional integrals, usually over the unit hypercube. They can be applied, at least in principle, to any simulation whose aim is to estimate a mathematical expectation. This covers a very wide range of applications. In this paper, we review some of the key ideas of quasi-Monte Carlo methods from a broad perspective, with emphasis on some recent results. We visit lattice rules in different types of spaces and make the connections between these rules and digital nets, thus covering the two most widely used QMC methods.