  A new method is described for constructing a generalized solution for
stochastic differential equations. The method is based on the Cameron-Martin
version of the Wiener Chaos expansion and provides a unified framework for the
study of ordinary and partial differential equations driven by finite- or
infinite-dimensional noise with either adapted or anticipating input.
Existence, uniqueness, regularity, and probabilistic representation of this
Wiener Chaos solution is established for a large class of equations. A number
of examples are presented to illustrate the general constructions. A detailed
analysis is presented for the various forms of the passive scalar equation and
for the first-order It\^{o} stochastic partial differential equation.
Applications to nonlinear filtering if diffusion processes and to the
stochastic Navier-Stokes equation are also discussed.
