Quasi-Monte Carlo algorithms for unbounded, weighted integration problems
In this article we investigate quasi-Monte Carlo (QMC) methods for multidimensional improper integrals with respect to a measure other than the uniform distribution. Additionally, the integrand is allowed to be unbounded at the lower boundary of the integration domain. We establish convergence of the QMC estimator to the value of the improper integral under conditions involving both the integrand and the sequence used. Furthermore, we suggest a modification of an approach proposed by Hlawka and Muck for the creation of low-discrepancy sequences with regard to a given density, which are suited for singular integrands. (C) 2003 Elsevier Inc. All rights reserved.
weighted integration quasi-monte carlo integration non-uniformly distributed low-discrepancy sequences