Diffusion processes with singular drift fields |
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| Authors: | Philippe Blanchard Simon Golin |
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| Affiliation: | (1) Department of Physics and Research Centre Bielefeld-Bochum-Stochastics, University of Bielefeld, D-4800 Bielefeld 1, Federal Republic of Germany;(2) Present address: Technische Universität Berlin, Fachbereich Mathematik MA 7-2, Strasse des 17. Juni 136, D-1000 Berlin 12 |
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| Abstract: | A class of stochastic differential equations with highly singular drift fields is considered. Using a purely probabilistic approach, we can show the unattainability of the nodal set. Moreover, a global existence and uniqueness theorem for diffusion processes with singular drift fields is established. The finite action condition of Carlen and Zheng can be modified. We relate our results to the diffusions which describe the time evolution of quantum systems in stochastic mechanics. |
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