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A one-dimensional diffusion hits points fast. (English) Zbl 1338.60197

Summary: A one-dimensional, continuous, regular, and strong Markov process \(X\) with state space \(E\) hits any point \(z\in E\) fast with positive probability. To wit, if \(\tau_z = \inf \{t \geq 0:X_{t} = z\}\), then \(\text{P}_{\xi}(\tau_z<\varepsilon)>0\) for all \(\xi \in E\) and \(\varepsilon >0\).

MSC:

60J60 Diffusion processes
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