Abstract
We regard a stochastic process as a weakly measurable function, taking values one of the Kondratiev Stochastic distribution spaces, (S)_{-\rho}. Since these spaces are duals of nuclear spaces, functions taking values in the dual of a nuclear space are treated in detail.
The space (S)_{-1} is a topological algebra with respect to the Wick product, ⋄, and the following relation hold,
∫Y(s)δη(s)=∫Y(s)⋄\dot{η}(s)ds.
As a consequence, we can regard SDEs as (S)_{-1}-valued ODEs. Similarily, we will regard an SPDE as an (S)_{-1}-valued PDE.