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

Martin Hairer (1) , Cyril Labbé (1)

1 WMI - Warwick Mathematics Institute

We propose a simple construction of the solution to the continuum parabolic Anderson model on $\mathbf{R}^2$ 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 $\mathbf{R}^2$.

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Martin Hairer, Cyril Labbé. A simple construction of the continuum parabolic Anderson model on $\mathbf{R}^2$. Electronic Communications in Probability, 2015, 20. ⟨hal-01427997⟩