Sufficient conditions for fast quasi-Monte Carlo convergence

Authors:
A. Papageorgiou
Affiliations:
Department of Computer Science, Columbia University, New York, NY
Venue:
Journal of Complexity
Year:
2003

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Abstract

We study the approximation of d-dimensional integrals. We present sufficient conditions for fast quasi-Monte Carlo convergence. They apply to isotropic and non-isotropic problems and, in particular, to a number of problems in computational finance. We show that the convergence rate of quasi-Monte Carlo is of order n-1+p{log n}-1/2 with p≥0. This is a worst case result. Compared to the expected rate n-1/2 of Monte Carlo it shows the superiority of quasi-Monte Carlo.