IJPAM: Volume 37, No. 1 (2007)
Department of Mathematics
Peterborough, Ontario, K9J 7B8, CANADA
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