A central limit theorem for branching Brownian motion with random immigration

We establish a central limit theorem for a branching Brownian motion with random immigration under the annealed law, where the immigration is determined by another branching Brownian motion. The limit is a Gaussian random measure and the normalization is t 3/4 for d = 3 and t 1/2 for d . 4, where in the critical dimension d = 4 both the immigration and the branching Brownian motion itself make contributions to the covariance of the limit.