Solving Stochastic Eigenvalue Problem of Wick Type

In this paper we study mathematically the eigenvalue
problem for stochastic elliptic partial differential equation of Wick
type. Using the Wick-product and the Wiener-Itô chaos expansion,
the stochastic eigenvalue problem is reformulated as a system of an
eigenvalue problem for a deterministic partial differential equation
and elliptic partial differential equations by using the Fredholm
alternative. To reduce the computational complexity of this system,
we shall use a decomposition method using the Wiener-Itô chaos
expansion. Once the approximation of the solution is performed using
the finite element method for example, the statistics of the numerical
solution can be easily evaluated.

• Hassan Manouzi
• Taous-Meriem Laleg-Kirati

• Eigenvalue problem
• Wick product
• SPDEs
• finite element
• Wiener-Itô chaos expansion.

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