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Conservative diffusions. (English) Zbl 0558.60059
This paper treats a mathematical problem arising in Nelson’s stochastic mechanics; the main result is an existence and uniqueness theorem for diffusions with extremely singular coefficients. The method of proof is based on several energy integral estimates derived here, and it can be considered as a time dependent generalization of the Dirichlet form method of constructing symmetric diffusion processes.
Further discussion and a cleaner proof that the path space measures constructed here are actually the laws of diffusion processes with the formally correct generator may be found in the author’s contribution to the BiBoS I symposium proceedings, to appear in Springer Lecture Notes in Mathematics.

MSC:
60J60 Diffusion processes
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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