Superprocesses with Dependent Spatial Motion and General Branching Densities

Donald A. Dawson, Zenghu Li and Hao Wang
Additional contact information
Donald A. Dawson: School of Mathematics and Statistics, Carleton University
Zenghu Li: Department of Mathematics, Beijing Normal University
Hao Wang: Department of Mathematics, University of Oregon

No lrsp-TRS346, RePAd Working Paper Series from Département des sciences administratives, UQO

Abstract: 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.

Keywords: superprocesses; interacting-branching particle system; diffusion process; martingale problem; dual process; rescaled limit; measure-valued catalyst (search for similar items in EconPapers)
JEL-codes: C10 C40 (search for similar items in EconPapers)
Date: 2001-01-01

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