On the attracting orbit of a nonlinear transformation arising from renormalization of hierarchically interacting diffusions. II: The non-compact case
type: Item
instance of: scholarly article
title: On the attracting orbit of a nonlinear transformation arising from renormalization of hierarchically interacting diffusions. II: The non-compact case
zbMATH Open document ID: 0873.60073
published in: Journal of Functional Analysis
publication date: 1997-06-23T00:00:00Z
review text: Motivated from the study of the space-time scaling limit of certain infinite system of interacting diffusion, this paper analyzes the \(n\)-fold composition of nonlinear integral operator acting on a class of functions on \([0,\infty)\). In part I [Can. J. Math. 47, No. 1, 3-27 (1995; Zbl 0832.60097)], the compact space \([0, 1]\) was treated. However, the non-compact case exhibits different behavior. The attracting orbits and attracting fixed points of the \(n\)-fold operator are identified and several convergences of the \(n\)-fold operator to the orbits or fixed points are characterized. For which, the authors present seven theorems, their proofs are analytic but rather technical and lengthy as one can imagine. However, the probabilistic meaning of the results are carefully explained.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 1013818
zbMATH Keywords: attracting orbit
zbMATH Keywords: attracting fixed point
zbMATH Keywords: order-preserving
author: J. B. Baillon
author: Philippe Clément
author: Andreas Greven
author: F. den Hollander
reviewed by: Mu-Fa Chen
MaRDI profile type: Publication
full work available at URL: jfan.1996.3031
OpenAlex ID: W1996321915
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DOI: 10.1006/JFAN.1996.3031
description: scientific article; zbMATH DE number 1013818