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Boundary Crossings of Brownian Motion

   
@article{ECP1155,
	author = {Enkelejd Hashorva},
	title = {Boundary Crossings of Brownian Motion},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {10},
	year = {2005},
	keywords = {},
	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 $t^*\in (0,1]$.},
	pages = {no. 21, 207-217},
	issn = {1083-589X},
	doi = {10.1214/ECP.v10-1155},    
        url = {http://ecp.ejpecp.org/article/view/1155}}