State Classification for a Class of Interacting Superprocesses with Location Dependent Branching

Abstract

The spatial structure of a class of superprocesses which arise as limits in distribution of a class of interacting particle systems with location dependent branching is investigated. The criterion of their state classification is obtained. Their effective state space is contained in the set of purely-atomic measures or the set of absolutely continuous measures according as one diffusive coefficient $c(x) \equiv 0$ or $|c(x)| \geq \epsilon \gt 0$ while another diffusive coefficient $h \in C^{2}_{b}(R)$.