On the Markov property for certain Gaussian random fields
type: Item
instance of: scholarly article
title: On the Markov property for certain Gaussian random fields
zbMATH Open document ID: 0592.60039
DOI: 10.1007/BF00699097
publication date: 1986-01-01T00:00:00Z
review text: It is well known that the so-called Markov property for random fields is an important ingredient in quantum field theory. Gaussian random fields associated with symmetric Markov processes were studied by E. B. Dynkin, who proved that the Markov property is at hand for the random field iff the Markov process has continuous paths. Later, \textit{M. Röckner} [see Math. Ann. 264, 153-177 (1983; Zbl 0519.60047)] gave an analytic proof of the same result in a slightly different formulation using the framework of Dirichlet spaces. In our article, a very simple proof of this result is presented. The main point is to use the ''fine topology'', and this is based on earlier results of the author. We also treat the connection between these random fields and certain infinite dimensional Ornstein- Uhlenbeck processes.
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 81P20
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 3951705
zbMATH Keywords: Markov property for random fields
zbMATH Keywords: quantum field theory
zbMATH Keywords: Gaussian random fields
zbMATH Keywords: symmetric Markov processes
zbMATH Keywords: Dirichlet spaces
zbMATH Keywords: infinite dimensional Ornstein-Uhlenbeck processes
author: Torbjoern Kolsrud
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3951705