Generalized Markov fields and Dirichlet forms
type: Item
instance of: scholarly article
title: Generalized Markov fields and Dirichlet forms
zbMATH Open document ID: 0588.60044
DOI: 10.1007/BF00047332
published in: Acta Applicandae Mathematicae
publication date: 1985-01-01T00:00:00Z
review text: The author considers a generalized Gaussian random field on a topological space for which the random field is indexed by measures and its covariance function is given by a transient Dirichlet form. He shows that this random field has the Markov property if and only if the Dirichlet form has the local property, by using potential theoretical methods. A similar result is shown in \textit{E. B. Dynkin} [Bull. Am. Math. Soc., New Ser. 3, 975-999 (1980; Zbl 0519.60046)].
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 81T99
zbMATH DE Number: 3944970
zbMATH Keywords: Gaussian random field
zbMATH Keywords: transient Dirichlet form
zbMATH Keywords: Markov property
zbMATH Keywords: potential theoretical methods
author: Michael Röckner
reviewed by: Shigeo Kusuoka
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00047332
OpenAlex ID: W2060055970
description: scientific article; zbMATH DE number 3944970