Super-Brownian motions in higher dimensions with absolutely continuous measure states
type: Item
instance of: scholarly article
title: Super-Brownian motions in higher dimensions with absolutely continuous measure states
zbMATH Open document ID: 0820.60032
DOI: 10.1007/BF02213461
author: Donald A. Dawson
author: Klaus Fleischmann
published in: Journal of Theoretical Probability
publication date: 1995-02-26T00:00:00Z
review text: Super-Brownian motions in two or more dimensions, with constant branching rates, are known to have singular measure states. There exist however much more general super-Brownian motions in which the random branching mechanism is determined by a non-negative continuous additive functional \(A\) of the Brownian motion. The main theorem of this paper shows that if certain technical conditions are imposed on \(A\), making the branching rate relatively irregular, then the resulting process has absolutely continuous measure states. The examples given by the authors to illustrate the applicability of the theorem have irregularities in only one coordinate. Such is for instance the case if \(A\) has a branching rate kernel determined along one coordinate by a typical realization of a stable subordinator with suitable index; this ensures that the branching effect is restricted to a dense set of parallel hyperplanes.
reviewed by: F. Papangelou
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 727282
zbMATH Keywords: super-Brownian motions
zbMATH Keywords: additive functional
zbMATH Keywords: realization of a stable subordinator
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 727282