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Diffusion processes with singular drift fields. (English) Zbl 0646.60066
Summary: 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 E. A. Carlen [ibid. 94, 293-315 (1984; Zbl 0558.60059)] and W. A. Zheng [Ann.Inst. Henri Poincaré, Probab. Stat. 21, 103-124 (1985; Zbl 0579.60050)] can be modified. We relate our results to the diffusions which describe the time evolution of quantum systems in stochastic mechanics.

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
81P20 Stochastic mechanics (including stochastic electrodynamics)
60J60 Diffusion processes
Full Text: DOI
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