Non Gaussian matrix-valued random fields for nonparametric probabilistic modeling of elliptic stochastic partial differential operators

Christian Soize (1)

1 LaM - Laboratoire de Mécanique

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.

Mots clés: stochastic elliptic operator; non gaussian; tensor valued random field

Domaines: Probabilités [math.PR]

Christian Soize. Non Gaussian matrix-valued random fields for nonparametric probabilistic modeling of elliptic stochastic partial differential operators. 9th ASCE Joint Speciality Conference on Probabilistic Mechanics and Structural Reliability, Sandia National Laboratory, Jul 2004, Albuquerque, New Mexico, United States. pp.1-6. ⟨hal-00688125⟩