Superprocesses with Dependent Spatial Motion and General Branching Densities
Donald A. Dawson, Carleton University
Zenghu Li, Beijing Normal University
Hao Wang, University of Oregon
Abstract
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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