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

摘要

The support properties of the super Brownian motion with random immigration X~ρ_t are considered, where the immigration rate is governed by the trajectory of another super-Brownian motion ρ. When both the initial state X~ρ_0 of the process and the immigration rate process ρ_0 are of finite measure and with compact supports, the probability of The support of the process X~ρ_t dominated by a ball is given by the solutions of a singular elliptic boundary value problem.