Limit theorems for occupation time fluctuations of branching systems I: Long-range dependence

AbstractWe give a functional limit theorem for the fluctuations of the rescaled occupation time process of a critical branching particle system in Rd with symmetric α-stable motion and α<d<2α, which leads to a long-range dependence process involving sub-fractional Brownian motion. We also give an analogous result for the system without branching and d