Renormalized-Generalized Solutions for the KPZ Equation

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.