Stochastic Differential Equations Driven by Purely Spatial Noise
Abstract
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 squareintegrable solution and must be solved in special weighted spaces. We demonstrate that the CameronMartin version of the Wiener chaos decomposition is an effective tool to study both stationary and evolution equations driven by spaceonly noise. The paper presents results about solvability of such equations in weighted Wiener chaos spaces and studies the longtime behavior of the solutions of evolution equations with spaceonly noise.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.math/0505551
 arXiv:
 arXiv:math/0505551
 Bibcode:
 2005math......5551L
 Keywords:

 Mathematics  Probability;
 Mathematics  Analysis of PDEs;
 60H40;
 35R60