A superprocess with a disappearing self-interaction
type: Item
instance of: scholarly article
title: A superprocess with a disappearing self-interaction
zbMATH Open document ID: 0841.60079
DOI: 10.1007/BF02213743
author: Robert J. Adler
author: Lidia Ivanitskaya
published in: Journal of Theoretical Probability
publication date: 1996-07-18T00:00:00Z
review text: The authors consider a system of independent branching Brownian motions, with a weak interaction between the particles, which affects the diffusion but not the branching. The interaction is chosen in such a way that it disappears at the limit when one considers the distribution of the superprocess \(X\). However the authors introduce processes which describe the diffusion part of the branching diffusion processes and prove that they converge in distribution to a process \(W\). Moreover, at the limit, the joint distribution of \((W,X)\) is absolutely continuous with respect to the noninteracting system, and not identical. So, while the pair \((X,W)\) does remember the interaction, it is only at the level of the joint distribution and not at the level of the marginal of the distribution of \(X\). The process \(W\) contains nevertheless useful information and is called by the authors ``ghost process''.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 847517
zbMATH Keywords: superprocesses
zbMATH Keywords: interacting particle systems
zbMATH Keywords: ghost process
reviewed by: Sylvie Méléard
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 847517