Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Efficiency improvement by lattice rules for pricing Asian options
Proceedings of the 30th conference on Winter simulation
Quasi-Monte Carlo algorithms for unbounded, weighted integration problems
Journal of Complexity
Halton Sequences Avoid the Origin
SIAM Review
Generating low-discrepancy sequences from the normal distribution: Box-Muller or inverse transform?
Mathematical and Computer Modelling: An International Journal
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To use quasi-Monte Carlo methods, the integral is usually first (implicitly) transformed to the unit cube. Integrals weighted with the multivariate normal density are usually transformed to the unit cube with the inverse of the multivariate normal cumulative distribution function. However, other transformations are possible, amongst which the transformation by Box and Muller. The danger in using a non-separable transformation is that it might break the low discrepancy structure which makes quasi-Monte Carlo converge faster than regular Monte Carlo. We examine several transformations visually, theoretically and practically and show that it is sometimes preferable to use other transformations than the inverse cumulative distribution function.