SUPER FRACTIONAL BROWNIAN-MOTION, FRACTIONAL SUPER BROWNIAN-MOTION AND RELATED SELF-SIMILAR (SUPER) PROCESSES

We consider the full weak convergence, in appropriate function spaces, of systems of noninteracting particles undergoing critical branching and following a self-similar spatial motion with stationary increments . The limit processes are measure-valued, and are of the super and his torical process type. In the case in which the underlying motion is th at of a fractional Brownian motion, we obtain a characterization of th e limit process as a kind of stochastic integral against the historica l process of a Brownian motion defined on the full real line.