A stochastic finite element method for stochastic parabolic equations driven by purely spatial noise

A Stochastic Finite Element Method for Stochastic Parabolic Equations Driven by Purely Spatial Noise

We consider parabolic SPDEs driven by purely spatial noise, and show the existence of solutions with random initial data and forcing terms. We perform error analysis for the semi-discrete stochastic finite element method applied to a class of equations with self-adjoint differential operators that are independent of time. The analysis employs the formal stochastic adjoint problem and the corres...

Stochastic Partial Differential Equations Driven by Purely Spatial Noise

We study bilinear stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron–Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven b...

Stochastic Differential Equations Driven by Purely Spatial Noise

Space-only noise is a natural random perturbation in equations without time evolution. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. The Cameron-Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven by space-only noise. The pape...

8 Stochastic Partial Differential Equations Driven by Purely Spatial Noise

We study bilinear stochastic parabolic and elliptic PDEs driven by purely spatial white noise. Even the simplest equations driven by this noise often do not have a square-integrable solution and must be solved in special weighted spaces. We demonstrate that the Cameron-Martin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven b...

The finite element method for a linear stochastic parabolic partial differential equation driven by additive noise