Discrepancy theory and quasi-Monte Carlo integration

Abstract

In this chapter we show the deep connectionsbetween discrepancytheory on the one hand and quasi-Monte Carlo integration on the other. Discrepancy theory was established as an area of research going back to the seminal paper by Weyl [117], whereas Monte Carlo (and later quasi-Monte Carlo) was invented in the 1940s by John von Neumann and Stanislaw Ulam to solve practical problems. The connection between these areas is well understood and will be presented here. We further include state of the art methods for quasi-Monte Carlo integration.