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

doi:10.1016/0304-4149(82)90030-8

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

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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 language	English (US)
Pages (from-to)	121-138
Number of pages	18
Journal	Stochastic Processes and their Applications
Volume	13
Issue number	2
DOIs	https://doi.org/10.1016/0304-4149(82)90030-8
State	Published - Aug 1982

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/0304-4149(82)90030-8

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

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.",

keywords = "Hermite polynomials, Hermite processes, Monte Carlo, Multigraph, hydrology, moments, self-similar processes",

author = "Taqqu, {Murad S.} and Goldberg, {Jeffrey B.}",

note = "Funding Information: by the National Science Foundation at Bell Telephone Laborator;-s.",

year = "1982",

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T1 - Regular multigraphs and their application to the Monte Carlo evaluation of moments of non-linear functions of Gaussian random variables

AU - Taqqu, Murad S.

AU - Goldberg, Jeffrey B.

N1 - Funding Information: by the National Science Foundation at Bell Telephone Laborator;-s.

PY - 1982/8

Y1 - 1982/8

N2 - 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.

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.

KW - Hermite polynomials

KW - Hermite processes

KW - Monte Carlo

KW - Multigraph

KW - hydrology

KW - moments

KW - self-similar processes

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DO - 10.1016/0304-4149(82)90030-8

M3 - Article

AN - SCOPUS:49049142125

SN - 0304-4149

VL - 13

SP - 121

EP - 138

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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