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G-2001-37

Randomized Polynomial Lattice Rules for Multivariate Integration and Simulation

and

BibTeX reference

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.

, 41 pages

This cahier was revised in November 2002

Publication

Randomized polynomial lattice tules for multivariate integration and simulation
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SIAM Journal on Scientific Computing, 24(5), 1768–1789, 2003 BibTeX reference