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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Communicated by A. Jaffe
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Blanchard, P., Golin, S. Diffusion processes with singular drift fields. Commun.Math. Phys. 109, 421–435 (1987). https://doi.org/10.1007/BF01206145
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DOI: https://doi.org/10.1007/BF01206145