Boundary Crossings of Brownian Motion

Enkelejd Hashorva (University of Bern, Switzerland)

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

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Pages: 207-217

Publication Date: October 3, 2005

DOI: 10.1214/ECP.v10-1155

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