A comparative study of Pseudo and Quasi random sequences for the solution intergral equations
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Random number generation and quasi-Monte Carlo methods
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A quasi-Monte Carlo approach to particle simulation of the heat equation
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Quasi-Monte Carlo methods in numerical finance
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A generalized discrepancy and quadrature error bound
Mathematics of Computation
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Monto Carlo extension of quasi-Monte Carlo
Proceedings of the 30th conference on Winter simulation
Efficiency improvement by lattice rules for pricing Asian options
Proceedings of the 30th conference on Winter simulation
Quasi-Monte Carlo via linear shift-register sequences
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American option pricing with randomized quasi-Monte Carlo simulations
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This article introduces Latin supercube sampling (LSS) for very high-dimensional simulations such as arise in particle transport, finance, and queueing. LSS is developed as a combination of two widely used methods: Latin hypercube sampling (LHS) and quasi-Monte Carlo (QMC). In LSS, the input variables are grouped into subsets, and a lower-dimensional QMC method is used within each subset. The QMC points are presented in random order within subsets. QMC methods have been observed to lose effectiveness in high-dimensional problems. This article shows that LSS can extend the benefits of QMC to much higher dimensions, when one can make a good grouping of input variables. Some suggestions for grouping variables are given for the motivating examples. Even a poor grouping can still be expected to do as well as LHS. The article also extends LHS and LSS to infinite-dimensional problems. The paper includes a survey of QMC methods, randomized versions of them (RQMC), and previous methods for extending QMC to higher dimensions. Furthermore it shows that LSS applied with RQMC is more reliable than LSS with QMC.