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 Aug 23

    Fingerprint

Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this