On the support of super-Brownian motion with super-Brownian immigration

The support properties of the super Brownian motion with random immigration X-t(rho) are considered, where the immigration rate is governed by the trajectory of another super-Brownian motion rho. When both the initial state X-0(rho) of the process and the immigration rate process rho (0) are of finite measure and with compact supports, the probability of the support of the process X-t(rho) dominated by a ball is given by the solutions of a singular elliptic boundary value problem.