Distribution of the Brownian motion on its way to hitting zero
Fima C. Klebaner (Monash University)
Abstract
For the one-dimensional Brownian motion $B=(B_t)_{t\geq 0}$, started at $x>0$, and the first hitting time $\tau=\inf\{t\geq 0:B_t=0\}$, we find the probability density of $B_{u\tau}$ for a $u\in(0,1)$, i.e. of the Brownian motion on its way to hitting zero.
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Pages: 641-648
Publication Date: December 17, 2008
DOI: 10.1214/ECP.v13-1432
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