Probability Theory and Related Fields

, Volume 83, Issue 3, pp 405–434

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


  • Sergio Albeverio
    • Institut für MathematikRuhr-Universität Bochum
    • Department of MathematicsUniversity of Edinburgh
  • Michael Röckner
    • Institut für MathematikRuhr-Universität Bochum

DOI: 10.1007/BF00964372

Cite this article as:
Albeverio, S. & Röckner, M. Probab. Th. Rel. Fields (1989) 83: 405. doi:10.1007/BF00964372


Given a (minimal) classical Dirichlet form onL2 (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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© Springer-Verlag 1989