We construct a class of superprocesses 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 arbitrary 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 special case that a suitable rescaled process of the superprocess converges to the usual super Brownian motion. An extension to measure-valued branching catalysts is also discussed.

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Electronic Journal of Probability
School of Mathematics and Statistics

Dawson, D.A, Li, Z. (Zenghu), & Wang, H. (Hao). (2001). Superprocesses with dependent spatial motion and general branching densities. Electronic Journal of Probability, 6, 1–33.