Superprocesses with Dependent Spatial Motion and General Branching Densities

We constructs a class of seperprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching density is given by an arbitary bounded non-negative Borel function, and the superprocess is characterized by a martingale problem as a diffusion process with state space "M (R)", improving and extending considerably the construction of Wang (1997, 1998). It is then proved in a spatial case that a suitable rescaled process of the superprocess converges to the usual super Brownian motion. An extention to measure-valued branching catalysts is also discussed.