We derive the asymptotic behavior of the total occupation measure of the unit ball for super-Brownian motion started from the Dirac measure at a distant point and conditioned to hit the unit ball. In the critical dimension 4, we obtain a limiting exponential distribution.
"On the occupation measure of super-Brownian motion." Electron. Commun. Probab. 11 252 - 265, 2006. https://doi.org/10.1214/ECP.v11-1225