Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Latin supercube sampling for very high-dimensional simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
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
The effective dimension and quasi-Monte Carlo integration
Journal of Complexity
Continuous random variate generation by fast numerical inversion
ACM Transactions on Modeling and Computer Simulation (TOMACS)
SIAM Journal on Scientific Computing
On simulation of tempered stable random variates
Journal of Computational and Applied Mathematics
Numerical inverse Lévy measure method for infinite shot noise series representation
Journal of Computational and Applied Mathematics
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An infinitely divisible random vector without Gaussian component admits representations of shot noise series. Due to possible slow convergence of the series, they have not been investigated as a device for Monte Carlo simulation. In this paper, we investigate the structure of shot noise series representations from a simulation point of view and discuss the effectiveness of quasi-Monte Carlo methods applied to series representations. The structure of series representations in nature tends to decrease their effective dimension and thus increase the efficiency of quasi-Monte Carlo methods, thanks to the greater uniformity of low-discrepancy sequence in the lower dimension. We illustrate the effectiveness of our approach through numerical results of moment and tail probability estimations for stable and gamma random variables.