A simple construction of the continuum parabolic anderson model on R2

Abstract

We propose a simple construction of the solution to the continuum parabolic Anderson model on R2 which does not rely on any elaborate arguments and makes extensive use of the linearity of the equation. A logarithmic renormalisation is required to counterbalance the divergent product appearing in the equation. Furthermore, we use time-dependent weights in our spaces of distributions in order to construct the solution on the unbounded space R2