A Unified Approach to Stochastic Evolution Equations Using the Skorokhod Integral
Probability
2007-09-20 v1 Analysis of PDEs
Abstract
We study stochastic evolution equations driven by Gaussian noise. The key features of the model are that the operators in the deterministic and stochastic parts can have the same order and the noise can be time-only, space-only, or space-time. Even the simplest equations of this kind 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 leads to natural weights and a natural replacement of the square integrability condition.
Keywords
Cite
@article{arxiv.0709.2975,
title = {A Unified Approach to Stochastic Evolution Equations Using the Skorokhod Integral},
author = {S. V. Lototsky and B. L. Rozovskii},
journal= {arXiv preprint arXiv:0709.2975},
year = {2007}
}