Regular multigraphs and their application to the Monte Carlo evaluation of moments of non-linear functions of Gaussian random variables

Murad S. Taqqu, Jeffrey B Goldberg

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper expands on the multigraph method for expressing moments of non-linear functions of Gaussian random variables. In particular, it includes a list of regular multigraphs that is needed for the computation of some of these moments. The multigraph method is then used to evaluate numerically the moments of non-Gaussian self-similar processes. These self-similar processes are of interest in various applications and the numerical value of their marginal moments yield qualitative information about the behavior of the probability tails of their marginal distributions.

Original languageEnglish (US)
Pages (from-to)121-138
Number of pages18
JournalStochastic Processes and their Applications
Volume13
Issue number2
DOIs
StatePublished - 1982
Externally publishedYes

Fingerprint

Multigraph
Random variables
Nonlinear Function
Random variable
Moment
Self-similar Processes
Evaluation
Tail Probability
Marginal Distribution
Expand
Evaluate
Tail probability

Keywords

  • Hermite polynomials
  • Hermite processes
  • hydrology
  • moments
  • Monte Carlo
  • Multigraph
  • self-similar processes

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Mathematics(all)
  • Modeling and Simulation
  • Statistics and Probability

Cite this

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AU - Taqqu, Murad S.

AU - Goldberg, Jeffrey B

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AB - This paper expands on the multigraph method for expressing moments of non-linear functions of Gaussian random variables. In particular, it includes a list of regular multigraphs that is needed for the computation of some of these moments. The multigraph method is then used to evaluate numerically the moments of non-Gaussian self-similar processes. These self-similar processes are of interest in various applications and the numerical value of their marginal moments yield qualitative information about the behavior of the probability tails of their marginal distributions.

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KW - Hermite processes

KW - hydrology

KW - moments

KW - Monte Carlo

KW - Multigraph

KW - self-similar processes

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