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Title: Quasi-Monte Carlo Method for Infinitely Divisible Random Vectors via Series Representations
Authors: Imai, Junichi
Kawai, Reiichiro
First Published: 24-Jun-2010
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Citation: SIAM Journal on Scientific Computing, 2010, 32 (4), pp. 1879-1897.
Abstract: 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.
DOI Link: 10.1137/090752365
ISSN: 1064-8275
Type: Article
Rights: This paper was published as SIAM Journal on Scientific Computing, 2010, 32 (4), pp. 1879-1897. It is also available from This paper appears here with the permission of SIAM. Doi: 10.1137/090752365
Appears in Collections:Published Articles, Dept. of Mathematics

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