This paper deals with the construction of a non Gaussian positive-definite matrix-valued random field whose mathematical properties allow elliptic stochastic partial differential operators to be modeled. Such a matrix- valued random field can directly be used for modeling random uncertainties in computational sciences with a stochastic model having a small number of parameters. The non Gaussian positive-definite matrix-valued random field presented in this paper allows such a probabilistic model of the fourth-order tensor-valued random field to be constructed and depends only of 4 scalar parameters: three spatial correlation lengths and one parameter allowing the level of the random fluctuations to be controlled. Such a model can directly be used in the stochastic finite element method.
Publié le : 2004-07-26
Classification:
stochastic elliptic operator,
non gaussian,
tensor valued random field,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00688125,
author = {Soize, Christian},
title = {Non Gaussian matrix-valued random fields for nonparametric probabilistic modeling of elliptic stochastic partial differential operators},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00688125}
}
Soize, Christian. Non Gaussian matrix-valued random fields for nonparametric probabilistic modeling of elliptic stochastic partial differential operators. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00688125/