H.-J. Starkloff: On the Dimensionality of the Stochastic Space in the Stochastic Finite Element Method

Author(s):

Hans-Jörg Starkloff

Title:

On the Dimensionality of the Stochastic Space in the Stochastic Finite Element Method

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 29, 2007

Mathematics Subject Classification:

60E05	[]
60H35	[]
60G12	[]

Abstract:

In recent works concerning the solution of various kinds of random equations or the stochastic simulation of random functions often so called (generalized) polynomial chaos expansions are used. Hereby one step is the representation of random variables through independent random variables with specific distributions, e.g., Gaussian variables. The present work addresses the questions how many such variables are needed and what kind of distributions can be generated in such a way. It is shown, that allowing arbitrary measurable transformations, usually one can generate the needed random variables with the help of only one random variable with continuous distribution function, e.g., one standard Gaussian random variable.

Keywords:

polynomial chaos, Gaussian Hilbert space, measurable transformation, random dimension, Monte Carlo methods

Language:

English

Publication time:

2007