Limit theorems for occupation time fluctuations of branching systems II: Critical and large dimensions

We give functional limit theorems for the fluctuations of the rescaled occupation time process of a critical branching particle system in RdRd with symmetric αα-stable motion in the cases of critical and large dimensions, d=2αd=2α and d>2αd>2α. In a previous paper [T. Bojdecki, L.G. Gorostiza, A. Talarczyk, Limit theorems for occupation time fluctuations of branching systems I: long-range dependence, Stochastic Process. Appl., this issue.] we treated the case of intermediate dimensions, ααd>α.