Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
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
Faster evaluation of multidimensional integrals
Computers in Physics
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
Complexity and information
Fast convergence of quasi-Monte Carlo for a class of isotropic integrals
Mathematics of Computation
Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
A constructive approach to strong tractability using Quasi-Monte Carlo algorithms
Journal of Complexity
The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension
Mathematics of Computation
Sufficient conditions for fast quasi-Monte Carlo convergence
Journal of Complexity
Open problems for tractability of multivariate integration
Journal of Complexity
Variance Reduction via Lattice Rules
Management Science
Mathematical and Computer Modelling: An International Journal
Smoothness and dimension reduction in Quasi-Monte Carlo methods
Mathematical and Computer Modelling: An International Journal
Remark on algorithm 659: Implementing Sobol's quasirandom sequence generator
ACM Transactions on Mathematical Software (TOMS)
Finite-order weights imply tractability of multivariate integration
Journal of Complexity
Journal of Complexity
Finite-order weights imply tractability of linear multivariate problems
Journal of Approximation Theory
Efficient simulated maximum likelihood with an application to online retailing
Statistics and Computing
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
Randomized Quasi-Monte Carlo: a tool for improving the efficiency of simulations in finance
WSC '04 Proceedings of the 36th 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
Complexity and effective dimension of discrete Lévy areas
Journal of Complexity
Research Note: Generating parallel quasirandom sequences via randomization
Journal of Parallel and Distributed Computing
Low discrepancy sequences in high dimensions: How well are their projections distributed?
Journal of Computational and Applied Mathematics
New Brownian bridge construction in quasi-Monte Carlo methods for computational finance
Journal of Complexity
Efficient Generation of Parallel Quasirandom Faure Sequences Via Scrambling
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Parallel quasirandom number generations for heterogeneous computing environments
International Journal of Parallel, Emergent and Distributed Systems
On efficient Monte Carlo-based statistical static timing analysis of digital circuits
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
On the approximation error in high dimensional model representation
Proceedings of the 40th Conference on Winter Simulation
Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing
INFORMS Journal on Computing
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Finite-order weights imply tractability of linear multivariate problems
Journal of Approximation Theory
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
On the optimal Halton sequence
Mathematics and Computers in Simulation
Dimension-wise integration of high-dimensional functions with applications to finance
Journal of Complexity
Practical Monte-Carlo based timing yield estimation of digital circuits
Proceedings of the Conference on Design, Automation and Test in Europe
Correlation controlled sampling for efficient variability analysis of analog circuits
Proceedings of the Conference on Design, Automation and Test in Europe
Computational investigations of scrambled Faure sequences
Mathematics and Computers in Simulation
Advanced variance reduction and sampling techniques for efficient statistical timing analysis
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Quasi-Monte Carlo Method for Infinitely Divisible Random Vectors via Series Representations
SIAM Journal on Scientific Computing
Evolutionary optimization of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Tuning the generation of sobol sequence with owen scrambling
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
On the use of dimension reduction techniques in quasi-Monte Carlo methods
Mathematical and Computer Modelling: An International Journal
Error Estimates for the ANOVA Method with Polynomial Chaos Interpolation: Tensor Product Functions
SIAM Journal on Scientific Computing
Enhancing Quasi-Monte Carlo Methods by Exploiting Additive Approximation for Problems in Finance
SIAM Journal on Scientific Computing
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Quasi-Monte Carlo (QMC) methods are successfully used for high-dimensional integrals arising in many applications. To understand this success, the notion of effective dimension has been introduced. In this paper, we analyse certain function classes commonly used in QMC methods for empirical and theoretical investigations and show that the problem of determining their effective dimension is analytically tractable. For arbitrary square integrable functions, we propose a numerical algorithm to compute their truncation dimension. We also consider some realistic problems from finance: the pricing of options. We study the special structure of the corresponding integrands by determining their effective dimension and show how large the effective dimension can be reduced and how much the accuracy of QMC estimates can be improved by using the Brownian bridge and the principal component analysis techniques. A critical discussion of the influence of these techniques on the QMC error is presented. The connection between the effective dimension and the performance of QMC methods is demonstrated by examples.