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math.ST updates on arXiv.org

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Distribution of the Brownian motion on its way to hitting zero
P. Chigansky, F. C. Klebaner · 2008-11-06 · via math.ST updates on arXiv.org

For the one-dimensional Brownian motion $B=(B_t)_{t\ge 0}$, started at $x>0$, and the first hitting time $τ=\inf\{t\ge 0:B_t=0\}$, we find the probability density of $B_{uτ}$ for a $u\in(0,1)$, i.e. of the Brownian motion on its way to hitting zero.

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