Wiener chaos solutions of linear stochastic evolution equations
arXiv:math/0504558 · doi:10.1214/009117905000000738
Abstract
A new method is described for constructing a generalized solution of a stochastic evolution equation. Existence, uniqueness, regularity and a probabilistic representation of this Wiener Chaos solution are established for a large class of equations. As an application of the general theory, new results are obtained for several types of the passive scalar equation.
Published at http://dx.doi.org/10.1214/009117905000000738 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)