A guide to simulation (2nd ed.)
A guide to simulation (2nd ed.)
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Efficiency improvement and variance reduction
WSC '94 Proceedings of the 26th conference on Winter simulation
Estimating security price derivatives using simulation
Management Science
Latin supercube sampling for very high-dimensional simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Tables of linear congruential generators of different sizes and good lattice structure
Mathematics of Computation
Fourier Analysis of Uniform Random Number Generators
Journal of the ACM (JACM)
Simulation Modeling and Analysis
Simulation Modeling and Analysis
Budget-Dependent Convergence Rate of Stochastic Approximation
SIAM Journal on Optimization
Variance Reduction via Lattice Rules
Management Science
On the Use of Quasi-Monte Carlo Methods in Computational Finance
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
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Quasi-Monte Carlo methods are designed to improve upon the Monte Carlo method for multidimensional numerical integration by using a more regularly distributed point set than the i.i.d. sample associated with Monte Carlo. Lattice rules are one family of quasi-Monte Carlo methods, originally proposed by Korobov in 1959. In this paper, we explain how randomized lattice rules can be used to construct efficient estimators for typical simulation problems, and we give several numerical examples. We are interested in two main aspects: Studying the variance of these estimators and finding which properties of the lattice rules should be considered when defining a selection criterion to rate and choose them. Our numerical results for three different problems illustrate how this methodology typically improves upon the usual Monte Carlo simulation method.