Randomized polynomial lattice rules for multivariate integration and simulation

Christiane Lemieux

doi:10.1137/S1064827501393782

Randomized polynomial lattice rules for multivariate integration and simulation

2003-01-01

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DOI：10.1137/S1064827501393782

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Lattice rules are among the best methods to estimate integrals in a large number of dimensions. They are part of the quasi-Monte Carlo set of tools. A theoretical framework for a class of lattice rules defined in a space of polynomials with coefficients in a finite field is developed in this paper. A randomized version is studied, implementations and criteria for selecting the parameters are discussed, and examples of its use as a variance reduction tool in stochastic simulation are provided. Certain types of digital net constructions, as well as point sets constructed by taking all vectors of successive output values produced by a Tausworthe random number generator, are special cases of this method.

Keywords:

numerical integration

lattice rules

variance reduction

quasi Monte Carlo

Randomized polynomial lattice rules for multivariate integration and simulation

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