Solving SPDEs driven by colored noise: a chaos approach
Probability
2007-06-25 v1 Analysis of PDEs
Abstract
An Ito-Skorokhod bi-linear equation driven by infinitely many independent colored noises is considered in a normal triple of Hilbert spaces. The special feature of the equation is the appearance of the Wick product in the definition of the Ito-Skorokhod integral, requiring innovative approaches to computing the solution. A chaos expansion of the solution is derived and several truncations of this expansion are studied. A recursive approximation of the solution is suggested and the corresponding approximation error bound is computed.
Cite
@article{arxiv.0706.3392,
title = {Solving SPDEs driven by colored noise: a chaos approach},
author = {S. V. Lototsky and K. Stemmann},
journal= {arXiv preprint arXiv:0706.3392},
year = {2007}
}