Acta Applicandae Mathematica

, Volume 3, Issue 3, pp 285–311

Generalized Markov fields and Dirichlet forms

  • Michael Röckner

DOI: 10.1007/BF00047332

Cite this article as:
Röckner, M. Acta Appl Math (1985) 3: 285. doi:10.1007/BF00047332


We prove that Gaussian measure-indexed random fields, of which the covariance functional is given by the dual form of a transient Dirichlet form, have the global Markov property (where ‘global’ here means ‘w.r.t. arbitrary, not necessarily open sets’), if and only if the Dirichlet form has the local property. Applications to Nelson's free Euclidean field of quantum theory and to Rozanov's generalized random functions are given.

AMS (MOS) subject classifications (1980)

Primary: 60G60secondary: 60J45

Key words

Markov propertyGaussian generalized fieldsprediction problemDirichlet spacesmeasures of bounded energybalayage of measurescapacitiesspectral synthesis

Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • Michael Röckner
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldWest Germany