## 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

### Keywords:

diffusion; hitting time; support
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