# Killed Rough Super-Brownian Motion

## TL;DR

This paper constructs the rough super-Brownian motion on finite volume with Dirichlet boundary conditions by analyzing the convergence of discrete approximations of the parabolic Anderson model.

## Contribution

It extends previous results to include finite volume settings with boundary conditions, advancing the understanding of rough super-Brownian motion.

## Key findings

- Successful construction of rough super-Brownian motion on finite volume
- Convergence results for discrete approximations of PAM on a box
- Extension of prior work to boundary condition scenarios

## Abstract

This note extends the results in [8] to construct the rough super-Brownian motion on finite volume with Dirichlet boundary conditions. The backbone of this study is the convergence of discrete approximations of the parabolic Anderson model (PAM) on a box.