Electronic Communications in Probability

Boundary Crossings of Brownian Motion

Enkelejd Hashorva

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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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