Proceedings of the 32nd conference on Winter simulation
Fast combined multiple recursive generators with multipliers of the form a = ±2q ±2r
Proceedings of the 32nd conference on Winter simulation
Software for uniform random number generation: distinguishing the good and the bad
Proceedings of the 33nd conference on Winter simulation
On the Use of Quasi-Monte Carlo Methods in Computational Finance
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Combined generators with components from different families
Mathematics and Computers in Simulation - Special issue: 3rd IMACS seminar on Monte Carlo methods - MCM 2001
A Dynamic Programming Procedure for Pricing American-Style Asian Options
Management Science
Quasi-monte carlo methods in practice: quasi-monte carlo methods for simulation
Proceedings of the 35th conference on Winter simulation: driving innovation
New simulation methodology for finance: efficient simulation of gamma and variance-gamma processes
Proceedings of the 35th conference on Winter simulation: driving innovation
Randomly shifted lattice rules on the unit cube for unbounded integrands in high dimensions
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
Quasi-Monte Carlo methods in finance
WSC '04 Proceedings of the 36th conference on Winter simulation
WSC '05 Proceedings of the 37th conference on Winter simulation
Randomly shifted lattice rules for unbounded integrands
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
Splitting for rare-event simulation
Proceedings of the 38th conference on Winter simulation
Rare events, splitting, and quasi-Monte Carlo
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Searching for extensible Korobov rules
Journal of Complexity
Low discrepancy sequences in high dimensions: How well are their projections distributed?
Journal of Computational and Applied Mathematics
Comparison of Point Sets and Sequences for Quasi-Monte Carlo and for Random Number Generation
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Approximate zero-variance simulation
Proceedings of the 40th Conference on Winter Simulation
A practical view of randomized quasi-Monte Carlo: invited presentation, extended abstract
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Randomly shifted lattice rules on the unit cube for unbounded integrands in high dimensions
Journal of Complexity - Special issue: Algorithms and complexity for continuous problems Schloss Dagstuhl, Germany, September 2004
Coupling from the past with randomized quasi-Monte Carlo
Mathematics and Computers in Simulation
A smooth estimator for MC/QMC methods in finance
Mathematics and Computers in Simulation
On the error distribution for randomly-shifted lattice rules
Winter Simulation Conference
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Evolutionary optimization of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Variance bounds and existence results for randomly shifted lattice rules
Journal of Computational and Applied Mathematics
Exact sampling with highly uniform point sets
Mathematical and Computer Modelling: An International Journal
Enhancing Quasi-Monte Carlo Methods by Exploiting Additive Approximation for Problems in Finance
SIAM Journal on Scientific Computing
Simulation of coalescence with stratified sampling
Proceedings of the Winter Simulation Conference
Constructing adapted lattice rules using problem-dependent criteria
Proceedings of the Winter Simulation Conference
Hi-index | 0.01 |
This is a review article on lattice methods for multiple integration over the unit hypercube, with a variance-reduction viewpoint. It also contains some new results and ideas. The aim is to examine the basic principles supporting these methods and how they can be used effectively for the simulation models that are typically encountered in the area of management science. These models can usually be reformulated as integration problems over the unit hypercube with a large (sometimes infinite) number of dimensions. We examine selection criteria for the lattice rules and suggest criteria which take into account the quality of the projections of the lattices over selected low-dimensional subspaces. The criteria are strongly related to those used for selecting linear congruential and multiple recursive random number generators. Numerical examples illustrate the effectiveness of the approach.