### Abstract

Let T_{1} denote the first passage time to 1 of a standard Brownian motion. It is well known that as λ → ∞, P(T_{1} > λ)∼ cλ^{−1/2}, where c = (2/π)^{1/2}. The goal of this note is to establish a capacitarian version of this result. Namely, we will prove the existence of positive and finite constants K1 and K2 such that for all λ > e^{e}, (formula presented) where ‘log’ denotes the natural logarithm, and Cap is capacity on Wiener space.

Original language | English |
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Pages (from-to) | 103-109 |

Number of pages | 7 |

Journal | Electronic Communications in Probability |

Volume | 4 |

DOIs | |

Publication status | Published - Jan 1 1999 |

### Keywords

- Brownian sheet
- Capacity on Wiener space
- Ornstein-Uhlenbeck process
- Quasi-sure analysis

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Csáki, E., Khoshnevisan, D., & Shi, Z. (1999). Capacity estimates, boundary crossings and the ornstein-uhlenbeck process in wiener space.

*Electronic Communications in Probability*,*4*, 103-109. https://doi.org/10.1214/ECP.v4-1011