Stochastic Differential Equations Driven by Purely Spatial Noise
概率论
2008-12-02 v3 偏微分方程分析
摘要
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.
引用
@article{arxiv.math/0505551,
title = {Stochastic Differential Equations Driven by Purely Spatial Noise},
author = {S. V. Lototsky and B. L. Rozovskii},
journal= {arXiv preprint arXiv:math/0505551},
year = {2008}
}