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|Title:||Quasi-Monte Carlo Method for Infinitely Divisible Random Vectors via Series Representations|
|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.|
|Rights:||This paper was published as SIAM Journal on Scientific Computing, 2010, 32 (4), pp. 1879-1897. It is also available from http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJOCE3000032000004001879000001&idtype=cvips&gifs=yes. 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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