This article concerns the construction of a continuous branching process in a random, time-independent environment, on finite volume. The backbone of this study is the convergence of discrete approximations of the parabolic Anderson model (PAM) on a box with Dirichlet boundary conditions. This is a companion paper to .
"Killed rough super-Brownian motion." Electron. Commun. Probab. 25 1 - 12, 2020. https://doi.org/10.1214/20-ECP319