Abstract.In recent years, quasi-Monte Carlo (QMC) integration methods have been successfully used in place of Monte-Carlo methods in many applications. However, in practice, QMC integration is often applied to integrands on unbounded domains with non-uniform probability measures, integrals for which there is little theoretical validation. We introduce group-theoretic methods to generate some non-uniform deterministic Weyl-like sequences. We also introduce a new importance sampling technique, which can be used with these group-theoretic sequences or lattice rules to create QMC integration rules with a high asymptotic order of convergence.

Received: March 6, 2007

AMS Subject Classification: 11K60, 65C05, 65C10, 65D32

Key Words and Phrases: quasi-Monte Carlo integration, non-uniform sequences, importance sampling, low-discrepancy sequences, Weyl sequences

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 37
Issue: 1