Non Gaussian matrix-valued random fields for nonparametric probabilistic modeling of elliptic stochastic partial differential operators
Résumé
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.
Domaines
Probabilités [math.PR]
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conference-2004-PMC2004-Albuquerque-soize.preprint.pdf (130.1 Ko)
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