Occupation time fluctuations of Poisson and equilibrium finite variance   branching systems
  Functional limit theorems are presented for the rescaled occupation time fluctuations process of a critical finite variance branching particle system in $R^d$ with symmetric a-stable motion starting off from either a standard Poisson random field or from the equilibrium distribution for intermediate dimensions a<d<2a. The limit processes are determined sub-fractional and fractional Brownian motion respectively. 
Piotr Milos