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

摘要

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 historical process type. In the case in which the underlying motion is that of a fractional Brownian motion, we obtain a characterization of the limit process as a kind of stochastic integral against the historical process of a Brownian motion defined on the full real line. [References: 15]