Quasi-Monte Carlo method for in finitely divisible random vectors via series representations

Junichi Imai, Reiichiro Kawai

Research output: Contribution to journalArticle

10 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1879-1897
Number of pages19
JournalSIAM Journal on Scientific Computing
Volume32
Issue number4
DOIs
Publication statusPublished - 2010

Fingerprint

Quasi-Monte Carlo Methods
Shot noise
Series Representation
Divisible
Random Vector
Shot Noise
Monte Carlo methods
Random variables
Low-discrepancy Sequences
Effective Dimension
Infinitely Divisible
Tail Probability
Series
Uniformity
Monte Carlo Simulation
Random variable
Tend
Moment
Numerical Results
Decrease

Keywords

  • Effective dimension
  • Gamma process
  • Moment estimation
  • Poisson process
  • Quasi-Monte Carlo method
  • Shot noise
  • Tail probability estimation

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

Quasi-Monte Carlo method for in finitely divisible random vectors via series representations. / Imai, Junichi; Kawai, Reiichiro.

In: SIAM Journal on Scientific Computing, Vol. 32, No. 4, 2010, p. 1879-1897.

Research output: Contribution to journalArticle

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