Normal (Gaussian) random variable for supercomputers
The Journal of Supercomputing
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Implementation and tests of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A quasi-Monte Carlo approach to particle simulation of the heat equation
SIAM Journal on Numerical Analysis
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Quasi-Random Sampling for Condensation
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
A Quasi-Monte Carlo Method for Integration with Improved Convergence
LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
Matrix Computations Using Quasirandom Sequences
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Sourcebook of parallel computing
Derivatives and credit risk: enhanced quasi-monte carlo methods with dimension reduction
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
New simulation methodology for finance: efficient simulation of gamma and variance-gamma processes
Proceedings of the 35th conference on Winter simulation: driving innovation
Probabilistically induced domain decomposition methods for elliptic boundary-value problems
Journal of Computational Physics
Quasi-Monte Carlo methods in finance
WSC '04 Proceedings of the 36th conference on Winter simulation
Inverting the symmetrical beta distribution
ACM Transactions on Mathematical Software (TOMS)
Hybrid method for the chemical master equation
Journal of Computational Physics
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
Simulation of a Lévy process by PCA sampling to reduce the effective dimension
Proceedings of the 40th Conference on Winter Simulation
Dimension Reduction Techniques in Quasi-Monte Carlo Methods for Option Pricing
INFORMS Journal on Computing
Acceleration of market value-at-risk estimation
Proceedings of the 2nd Workshop on High Performance Computational Finance
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
Dimension-wise integration of high-dimensional functions with applications to finance
Journal of Complexity
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A superconvergent monte carlo method for multiple integrals on the grid
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
Fast orthogonal transforms and generation of Brownian paths
Journal of Complexity
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
American option pricing with randomized quasi-Monte Carlo simulations
Proceedings of the Winter Simulation Conference
Journal of Computational Physics
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Monte Carlo integration using quasirandom sequences has theoretical error bounds of size O (N^-^1 log^dN) in dimension d, as opposed to the error of size O (N^-^1^2) for random or pseudorandom sequences. In practice, however, this improved performance for quasirandom sequences is often not observed. The degradation of performance is due to discontinuity or lack of smoothness in the integrand and to large dimension of the domain of integration, both of which often occur in Monte Carlo methods. In this paper, modified Monte Carlo methods are developed, using smoothing and dimension reduction, so that the convergence rate of nearly O (N^-^1) is regained. The standard rejection method, as used in importance sampling, involves discontinuities, corresponding to the decision to accept or reject. A smoothed rejection method, as well as a method of weighted uniform sampling, is formulated below and found to have error size of almost O (N^-^1) in quasi-Monte Carlo. Quasi-Monte Carlo evaluation of Feynman-Kac path integrals involves high dimension, one dimension for each discrete time interval. Through an alternative discretization, the effective dimension of the integration domain is drastically reduced, so that the error size close to O(N^-^1) is again regained.