Superprocesses with Dependent Spatial Motion and General Branching Densities
Probability
2011-02-19 v1
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 , 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.
Cite
@article{arxiv.math/0606615,
title = {Superprocesses with Dependent Spatial Motion and General Branching Densities},
author = {Donald A. Dawson and Zenghu Li and Hao Wang},
journal= {arXiv preprint arXiv:math/0606615},
year = {2011}
}