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
  • Michael Röckner

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).

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Sergio Albeverio
    • 1
    • 2
  • Michael Röckner
    • 1
  1. 1.Institut für MathematikRuhr-Universität BochumBochum 1Federal Republic of Germany
  2. 2.Department of MathematicsUniversity of EdinburghEdinburghScotland
  3. 3.(Bochum-Essen-Düsseldorf)
  4. 4.BiBoS Research CentreCERFIM Research Centre(Locarno)