Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
The mean square discrepancy of randomized nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Monte Carlo Variance of Scrambled Net Quadrature
SIAM Journal on Numerical Analysis
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
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Journal of Complexity
The asymptotic efficiency of randomized nets for quadrature
Mathematics of Computation
Erratum: Quadrature Error Bounds with Applications to Lattice Rules
SIAM Journal on Numerical Analysis
The Mean Square Discrepancy of Scrambled (t,s)-Sequences
SIAM Journal on Numerical Analysis
Algorithm 823: Implementing scrambled digital sequences
ACM Transactions on Mathematical Software (TOMS)
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
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
Rare events, splitting, and quasi-Monte Carlo
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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Proceedings of the 40th Conference on Winter Simulation
Simulation of a Lévy process by PCA sampling to reduce the effective dimension
Proceedings of the 40th Conference on Winter Simulation
Coupling from the past with randomized quasi-Monte Carlo
Mathematics and Computers in Simulation
Computational investigations of scrambled Faure sequences
Mathematics and Computers in Simulation
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Tuning the generation of sobol sequence with owen scrambling
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Constructions of (t ,m,s)-nets and (t,s)-sequences
Finite Fields and Their Applications
American option pricing with randomized quasi-Monte Carlo simulations
Proceedings of the Winter Simulation Conference
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There have been many proposals for randomizations of digital nets. Some of those proposals greatly reduce the computational burden of random scrambling. This article compares the sampling variance under different scrambling methods. Some scrambling methods adversely affect the variance, even to the extent of deteriorating the rate at which variance converges to zero. Surprisingly, a new scramble proposed here, has the effect of improving the rate at which the variance converges to zero, but so far, only for one dimensional integrands. The mean squared L2 discrepancy is commonly used to study scrambling schemes. In this case, it does not distinguish among some scrambles with different convergence rates for the variance.