Quasi-monte carlo methods in practice: quasi-monte carlo methods for simulation

Authors:
Pierre L'Ecuyer
Affiliations:
Université de Montréal, Montréal (Québec), Canada
Venue:
Proceedings of the 35th conference on Winter simulation: driving innovation
Year:
2003

Citing 15
Cited 1

Random number generation and quasi-Monte Carlo methods

Random number generation and quasi-Monte Carlo methods
Imbedded lattice rules for multidimensional integration

SIAM Journal on Numerical Analysis
Quasi-random methods for estimating integrals using relatively small samples

SIAM Review
Algorithm 659: Implementing Sobol's quasirandom sequence generator

ACM Transactions on Mathematical Software (TOMS)
Latin supercube sampling for very high-dimensional simulations

ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
A generalized discrepancy and quadrature error bound

Mathematics of Computation
Variance reduction order using good lattice points in Monte Carlo methods

Computing
Generating Quasi-Random Paths for Stochastic Processes

SIAM Review
Lattice computations for random numbers

Mathematics of Computation
On selection criteria for lattice rules and other quasi-Monte Carlo point sets

Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
The Art of Computer Programming Volumes 1-3 Boxed Set

The Art of Computer Programming Volumes 1-3 Boxed Set
Extensible Lattice Sequences for Quasi-Monte Carlo Quadrature

SIAM Journal on Scientific Computing
Randomized Polynomial Lattice Rules for Multivariate Integration and Simulation

SIAM Journal on Scientific Computing
Variance with alternative scramblings of digital nets

ACM Transactions on Modeling and Computer Simulation (TOMACS)
Variance Reduction via Lattice Rules

Management Science

New simulation methodology for finance: efficient simulation of gamma and variance-gamma processes

Proceedings of the 35th conference on Winter simulation: driving innovation

Quantified Score

Hi-index	0.00

Visualization

Abstract

Quasi-Monte Carlo (QMC) methods are numerical techniques for estimating large-dimensional integrals, usually over the unit hypercube. They can be applied, at least in principle, to any simulation whose aim is to estimate a mathematical expectation. This covers a very wide range of applications. In this paper, we review some of the key ideas of quasi-Monte Carlo methods from a broad perspective, with emphasis on some recent results. We visit lattice rules in different types of spaces and make the connections between these rules and digital nets, thus covering the two most widely used QMC methods.