Continuous dependence of a class of superprocesses on branching parameters and applications
type: Item
instance of: scholarly article
title: Continuous dependence of a class of superprocesses on branching parameters and applications
zbMATH Open document ID: 0938.60078
author: Donald A. Dawson
author: Klaus Fleischmann
author: Guillaume Leduc
published in: The Annals of Probability
publication date: 2000-06-08T00:00:00Z
review text: This paper discusses the dependence of a finite-variance \((\xi,\Phi,k)\)-superprocess \(X\) on the branching mechanism \(\Phi(s,x,\lambda)\) and on the branching additive functional \(k(ds)\). In the general case where the one-particle motion \(\xi\) is a right process with càdlàg sample paths in a metrizable Luzin space \(E\), continuity of \(X\) with respect to \((\Phi,k)\) is obtained in the sense of convergence of the finite-dimensional marginals. Under the assumption that \(E\) is compact and \(\xi\) is a Hunt process, this result is sharpened to weak continuity of the law of \(X\) on Skorokhod space. In the latter context it is also shown that \(X\) itself possesses the Hunt property.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60J40
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 1355247
zbMATH Keywords: superprocess
zbMATH Keywords: branching functional
zbMATH Keywords: catalytic branching
zbMATH Keywords: convergence of processes
zbMATH Keywords: Hunt process
reviewed by: Alexander Schied
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1022855644
OpenAlex ID: W1537929748
DOI: 10.1214/AOP/1022855644
description: scientific article; zbMATH DE number 1355247