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Classical dirichlet forms on topological vector spaces-the construction of the associated diffusion process
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  • Published: September 1989

Classical dirichlet forms on topological vector spaces-the construction of the associated diffusion process

  • Sergio Albeverio1,2 nAff3 &
  • Michael Röckner1 nAff4 

Probability Theory and Related Fields volume 83, pages 405–434 (1989)Cite this article

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Summary

Given a (minimal) classical Dirichlet form onL 2 (E;μ) we construct the associated diffusion process. HereE is a locally convex topological vector space and μ is a (not necessarily quasi-invariant) probability measure onE. The construction is carried out under certain assumptions onE and μ which can be easily verified in many examples. In particular, we explicitly apply our results to (time-zero and space-time) quantum fields (with or with-out cut-off).

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Author information

Author notes
  1. Sergio Albeverio

    Present address: , SFB 237, (Bochum-Essen-Düsseldorf)

  2. Michael Röckner

    Present address: BiBoS Research Centre, CERFIM Research Centre, (Locarno)

Authors and Affiliations

  1. Institut für Mathematik, Ruhr-Universität Bochum, D-4630, Bochum 1, Federal Republic of Germany

    Sergio Albeverio & Michael Röckner

  2. Department of Mathematics, University of Edinburgh, EH9 3JZ, Edinburgh, Scotland

    Sergio Albeverio

Authors
  1. Sergio Albeverio
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  2. Michael Röckner
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Additional information

Dedication: Raphael Høegh-Krohn (1938–1988) was an initiator of the theory of Dirichlet forms over infinite dimensional spaces. He has been a continuous source of inspiration. We deeply mourn his departure and dedicate to him this work, as a small sign of our great gratitude

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Albeverio, S., Röckner, M. Classical dirichlet forms on topological vector spaces-the construction of the associated diffusion process. Probab. Th. Rel. Fields 83, 405–434 (1989). https://doi.org/10.1007/BF00964372

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  • Received: 02 December 1988

  • Revised: 22 March 1989

  • Issue Date: September 1989

  • DOI: https://doi.org/10.1007/BF00964372

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Keywords

  • Vector Space
  • Stochastic Process
  • Probability Measure
  • Probability Theory
  • Diffusion Process
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