A one-dimensional diffusion hits points fast

Cameron Bruggeman; Johannes Ruf

A one-dimensional diffusion hits points fast

Probability 2015-08-18 v1

Authors: Cameron Bruggeman , Johannes Ruf

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 $\varepsilon>0$ .

Keywords

diffusion processes markov processes

Cite

@article{arxiv.1508.03822,
  title  = {A one-dimensional diffusion hits points fast},
  author = {Cameron Bruggeman and Johannes Ruf},
  journal= {arXiv preprint arXiv:1508.03822},
  year   = {2015}
}

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