Open Access
2005 Boundary Crossings of Brownian Motion
Enkelejd Hashorva
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Electron. Commun. Probab. 10: 207-217 (2005). DOI: 10.1214/ECP.v10-1155


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 $t^*\in (0,1]$.


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Enkelejd Hashorva. "Boundary Crossings of Brownian Motion." Electron. Commun. Probab. 10 207 - 217, 2005.


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

zbMATH: 1110.60076
MathSciNet: MR2175400
Digital Object Identifier: 10.1214/ECP.v10-1155

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