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Limit at zero of the Brownian first-passage density

By Goran Peskir


Let (Bt)t 0 be a standard Brownian motion started at zero, let g: IR+! IR be an upper function for B satisfying g(0) = 0, and let = inf f t> 0 j Bt g(t) g be the first-passage time of B over g. Assume that g is C 1 on 0;1, increasing (locally at zero), and concave (locally at zero). Then the following identities hold for the density function f of: f(0+) = lim t#0 1 2 g(t) t3=2 g(t

Year: 2001
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