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.
S. V. Lototsky. B. L. Rozovskii. "Wiener chaos solutions of linear stochastic evolution equations." Ann. Probab. 34 (2) 638 - 662, March 2006. https://doi.org/10.1214/009117905000000738