8 Stochastic Partial Differential Equations Driven by Purely Spatial Noise

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...

ar X iv : m at h / 05 05 55 1 v 2 [ m at h . PR ] 1 6 Ju n 20 07 STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY PURELY SPATIAL NOISE

We study 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 by space-o...

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...

dlw2 (2003/04/06) A degenerate stochastic partial differential equation for the purely atomic superprocess with dependent spatial motion

A purely atomic superprocess with dependent spatial motion is characterized as the pathwise unique solution of a stochastic partial differential equation, which is driven by a time-space white noise defining the spatial motion and a sequence of independent Brownian motions defining the branching mechanism. AMS Subject Classifications: Primary 60J80, 60G57; Secondary 60J35

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion