Lipschitzian complete error calculus and Dirichlet forms
type: Item
instance of: scholarly article
title: Lipschitzian complete error calculus and Dirichlet forms
zbMATH Open document ID: 1031.31005
DOI: 10.1016/S0021-7824(01)01206-5
author: Nicolas Bouleau
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2002-07-24T00:00:00Z
review text: Taking as a starting point Gauss' error calculus (for differentiable functions), the author points out a certain coherence property. In order to extend Gauss' quadratic formula to Lipschitz functions, a reinforced coherence principle is considered and an axiomatic error structure is proposed, in which a Dirichlet form appears [\textit{A. Beurling} and \textit{J. Deny}, Acta Math. 99, 203-224 (1958; Zbl 0089.08106)]. One gets a Lipschitzian complete error calculus, which behaves well by images and by products and also from the point of view of links with experiments; it is suitable, in particular, for infinite-dimensional models met in stochastic analysis. This error calculus is connected with statistics by means of the notion of Fisher information matrix. Three consistent examples for this axiomatic structure are presented. Projective systems of such objects are also considered, in order to catch the delicate question of error permanency, discovered by Poincaré. Finally, a list of conjectures is discussed.
reviewed by: Liliana Popa
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 62B15
zbMATH DE Number: 1770853
zbMATH Keywords: error
zbMATH Keywords: Dirichlet form
zbMATH Keywords: squared field operator
zbMATH Keywords: Lipschitz calculus
zbMATH Keywords: Fisher information matrix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1770853