Stochastic Partial Differential Equations and Renormalization à la
We present a novel framework for the study of a large class of non-linear
stochastic partial differential equations, which is inspired by the algebraic
approach to quantum field theory. The main merit is that, by realizing random
fields within a suitable algebra of functional-valued distributions, we are able
to use specific techniques proper of microlocal analysis. These allow us to deal
with renormalization using an Epstein-Glaser perspective, hence without
resorting to any specific regularization scheme. As a concrete example we shall
use this method to discuss both the stochastic $Phi^3_d$ model and the
non-linear Schroedinger equation.
Talk based on
 C.D., Nicolò Drago, Paolo Rinaldi & Lorenzo Zambotti, Commun.
Contemp. Math. 24 (2022), no. 7, Paper No. 2150075,
 Alberto Bonicelli, C.D. & Paolo Rinaldi,