S. V. Lototsky, B. L. Rozovskii
Published 2005-05-25, updated 2008-12-02Version 3
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-only noise. The paper presents results about solvability of such equations in weighted Wiener chaos spaces and studies the long-time behavior of the solutions of evolution equations with space-only noise.
On stochastic differential equations driven by the renormalized square of the Gaussian white noise
Stochastic differential equations driven by loops
Strong approximation of stochastic differential equations driven by a time-changed Brownian motion with time-space-dependent coefficients
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