A simple construction of the continuum parabolic Anderson model on $\mathbf{R}^2$

摘要: We propose a simple construction of the solution to continuum parabolic Anderson model on $\mathbf{R}^2$ which does not rely any elaborate arguments and makes extensive use linearity equation. A logarithmic renormalisation is required counterbalance divergent product appearing in Furthermore, we time-dependent weights our spaces distributions order construct unbounded space $\mathbf{R}^2$.