Probability Theory and Related Fields

, Volume 83, Issue 3, pp 405-434

First online:

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

  • Sergio AlbeverioAffiliated withInstitut für Mathematik, Ruhr-Universität BochumDepartment of Mathematics, University of Edinburgh
  • , Michael RöcknerAffiliated withInstitut für Mathematik, Ruhr-Universität Bochum

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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).