Randomly shifted lattice rules on the unit cube for unbounded integrands in high dimensions (Q2489151)

This paper is concerned with quasi-Monte Carlo (QMC) integration on the unit cube for unbounded integrands. The worst-case error is studied for randomly shifted rank-1 lattice rules in a weighted tensor-product reproducing kernel Hilbert space, which possesses a specified boundary behavior of the unbounded integrands and the desired robustness property of QMC is established. Then a component-by-component algorithm of randomly shifted lattice rules is presented to achieve the worst-case error bound of order \(O(n^{-1/2})\). Two numerical experiments are presented to illustrate the proposed lattice rules. The limitation of the proposed algorithm is also discussed.