  A mild formulation for stochastic parabolic Anderson model with
time-homogeneous Gaussian potential suggests a way of defining a solution to
obtain its optimal regularity. Two different interpretations in the equation or
in the mild formulation are possible with usual pathwise product and the Wick
product: the usual pathwise interpretation is mainly discussed. We emphasize
that a modified version of parabolic Schauder estimates is a key idea for the
existence and uniqueness of a mild solution. In particular, the mild
formulation is crucial to investigate a relation between the equation with
usual pathwise product and the Wick product.
