Abstract Markov property and local operators
type: Item
instance of: scholarly article
title: Abstract Markov property and local operators
zbMATH Open document ID: 0868.60044
author: Jörg Schäfer
published in: Journal of Functional Analysis
publication date: 1996-06-16T00:00:00Z
review text: Generalized random fields with certain Markov properties are constructed. To unify the different approaches to the notions of Markov property, the author defines a general set-up, including different index sets, and a suitable Markov property called ``abstract'' Markov property. This set-up is formulated in the context of manifolds and bundle-sections. It is proved the preservation of the abstract Markov property for local operators on specific vector spaces. Under some assumptions on the index spaces involved the author discusses the preseparation of the \(c\)-Markov property. The illustrative examples are taken from quantum field theory. In the last section, the relation between different Markov properties is clarified.
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 889771
zbMATH Keywords: Markov random processes
zbMATH Keywords: linear maps
zbMATH Keywords: Markov property
zbMATH Keywords: Dirac equation
zbMATH Keywords: Markov random fields
zbMATH Keywords: inhomogeneous Cauchy-Riemann equation
MaRDI profile type: Publication
full work available at URL: jfan.1996.0059
OpenAlex ID: W1990819404
DOI: 10.1006/JFAN.1996.0059
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description: scientific article; zbMATH DE number 889771