  This work introduces a new notion of solution for the KPZ equation, in
particular, our approach encompasses the Cole-Hopf solution. We set in the
context of the distribution theory the proposed results by Bertini and Giacomin
from the mid 90's.
  This new approach provides a pathwise notion of solution as well as a
structured approximation theory. The developments are based on regularization
arguments from the theory of distributions.
