Approximation of Quasi-Monte Carlo worst case error in weighted spaces of infinitely times smooth functions

摘要

In this paper, we consider Quasi-Monte Carlo (QMC) worst case error of weighted smooth function classes in C∞[0,1]s by a digital net over F2. We show that the ratio of the worst case error to the QMC integration error of an exponential function is bounded above and below by constants. This result provides us with a simple interpretation that a digital net with small QMC integration error for an exponential function also gives the small integration error for any function in this function space.