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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.

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