Bojdecki, T.; Gorostiza, Luis G.; Talarczyk, A. - Départment des sciences administratives, Université … - 2005
We prove a functional limit theorem for the rescaled occupation time fluctuations of a (d, , )- branching particle system (particles moving in Rd according to a symmetric -stable L´evy process, branching law in the domain of attraction of a (1 + )-stable law, 0 < < 1, uniform Poisson initial state) in the case of intermediate dimensions, / < d < (1 + )/. The limit is a process of the form K, where K is a constant, is the Lebesgue measure on Rd, and = (t)t0 is a (1+)-stable process which has long range dependence. There are two long range dependence regimes, one for all > d/(d + ), which coincides with...</<>