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Numerical solutions of SPDEs involving white noise

Hassan Manouzi

Abstract


The purpose of this paper is to give a weak formulation of linear stochastic partial differential equations (SPDEs) in infinite dimension driven by a space-time white noise under the framework of the white noise analysis. We give existence and uniqueness results for the continuous problem. Our method will reduce the problem of solving SPDEs to solving a set of deterministic ones. Moreover, one can reconstruct particular realizations of the solution directly from Wiener chaos expansions once the coefficients are available.

Keywords


Finite element method, Stochastic partial differential equations, Stochastic simulation, white noise, Wick product.

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