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