## Electronic Communications in Probability

### Boundary Crossings of Brownian Motion

Enkelejd Hashorva

#### Abstract

Let $B$ be a standard Brownian motion and let $b_\gamma$ be a piecewise linear continuous boundary function. In this paper we obtain an exact asymptotic expansion of $P\{ B(t) < b_\gamma(t), \forall t\in [0,1]\}$ provided that the boundary function satisfies $\lim_{\gamma \to \infty} b_\gamma(t^*)= -\infty$ for some $t^*\in (0,1]$.

#### Article information

Source
Electron. Commun. Probab., Volume 10 (2005), paper no. 21, 207-217.

Dates
Accepted: 3 October 2005
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465058086

Digital Object Identifier
doi:10.1214/ECP.v10-1155

Mathematical Reviews number (MathSciNet)
MR2175400

Zentralblatt MATH identifier
1110.60076

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

#### Citation

Hashorva, Enkelejd. Boundary Crossings of Brownian Motion. Electron. Commun. Probab. 10 (2005), paper no. 21, 207--217. doi:10.1214/ECP.v10-1155. https://projecteuclid.org/euclid.ecp/1465058086

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