Dimension-wise Multivariate Orthogonal Polynomials in General Probability Spaces

Sharif Rahman

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Dimension-wise Multivariate Orthogonal Polynomials in General Probability Spaces

Preprint

Open access

Dimension-wise Multivariate Orthogonal Polynomials in General Probability Spaces

Sharif Rahman

ArXiv.org

10/26/2018

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url

https://arxiv.org/abs/1810.12113\nView

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the existing PDD, which is valid strictly for independent random variables, no tensor-product structure is assumed or required. Important mathematical properties of GPDD are studied by constructing dimension-wise decomposition of polynomial spaces, deriving statistical properties of random orthogonal polynomials, demonstrating completeness of orthogonal polynomials for prescribed assumptions, and proving mean-square convergence to the correct limit, including when there are infinitely many random variables. The GPDD approximation proposed should be effective in solving high-dimensional stochastic problems subject to dependent variables.

Details

Title: Subtitle: Dimension-wise Multivariate Orthogonal Polynomials in General Probability Spaces
Creators: Sharif Rahman
Resource Type: Preprint
Publication Details: ArXiv.org
ISSN: 2331-8422
Language: English
Date posted: 10/26/2018
Academic Unit: Mechanical Engineering
Record Identifier: 9984201537402771

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