A one-dimensional diffusion hits points fast

Published 16 Aug 2015 in math.PR | (1508.03822v1)

Abstract: 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 $P_\xi({ \tau}_z<\varepsilon)>0$ for all $\xi \in E$ and $\varepsilon>0$.

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