Super Brownian motion is known to occur as the limit of properly rescaled interacting particle systems such as branching random walk, the contact process and the voter model.
In this paper we show that certain linearly interacting diffusions converge to super Brownian motion if suitably rescaled in time and space. The results comprise nearest neighbor interaction as well as long range interaction.
"Rescaled interacting diffusions converge to super Brownian motion." Ann. Appl. Probab. 13 (2) 501 - 514, May 2003. https://doi.org/10.1214/aoap/1050689591