Open Access
2016 A one-dimensional diffusion hits points fast
Cameron Bruggeman, Johannes Ruf
Electron. Commun. Probab. 21: 1-7 (2016). DOI: 10.1214/16-ECP4544


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 ${\boldsymbol{\tau } }_z = \inf \{t \geq 0:X_{t} = z\}$, then $\textsf{P} _\xi ({\boldsymbol{\tau } }_z<\varepsilon )>0$ for all $\xi \in E$ and $\varepsilon >0$.


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Cameron Bruggeman. Johannes Ruf. "A one-dimensional diffusion hits points fast." Electron. Commun. Probab. 21 1 - 7, 2016.


Received: 8 September 2015; Accepted: 25 February 2016; Published: 2016
First available in Project Euclid: 10 March 2016

zbMATH: 1338.60197
MathSciNet: MR3485391
Digital Object Identifier: 10.1214/16-ECP4544

Primary: 60J60

Keywords: diffusion , hitting time , Support

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