Absolute continuity of catalytic measure-valued branching processes.
type: Item
instance of: scholarly article
title: Absolute continuity of catalytic measure-valued branching processes.
zbMATH Open document ID: 1045.60036
DOI: 10.1016/S0304-4149(00)00022-3
author: Achim Klenke
published in: Stochastic Processes and their Applications
publication date: 2004-09-07T00:00:00Z
review text: A catalytic measure-valued branching process in \(\mathbb R^d\) with a Feller motion process \(\xi \) is studied, where the branching rate is given by a continuous additive functional of \(\xi \) and where the branching law may vary in space and time. A sufficient condition for absolute continuity of the values of the process with respect to Lebesgue measure is given. The condition is sharp for the classical cases. Conversely, a sufficient condition for singularity of the states is also provided.
Mathematics Subject Classification ID: 60G30
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 2098350
zbMATH Keywords: interacting particle systems
zbMATH Keywords: super-Brownian motion
zbMATH Keywords: absolute continuity
MaRDI profile type: Publication
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full work available at URL: s0304-4149(00)00022-3
OpenAlex ID: W2086228805
description: scientific article; zbMATH DE number 2098350