Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems

Several long-range dependence, self-similar Gaussian processes arise from asymptotics of some classes of spatially distributed particle systems and superprocesses. The simplest examples are fractional Brownian motion and sub-fractional fractional Brownian motion, the latter being intermediate between Brownian motion and fractional Brownian motion. In this paper we focus mainly on long-range dependence processes that arise from occupation time fluctuations of immigration particle systems with or without branching, and we study their properties. Some long-range dependence non-Gaussian processes that appear in a similar way are also mentioned.