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arXiv · 0811.0909

Distribution of the Brownian motion on its way to hitting zero

P. Chigansky·F. C. Klebaner
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Abstract

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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P. Chigansky, F. C. Klebaner. 2008-12-18. Distribution of the Brownian motion on its way to hitting zero. https://arxiv.org/abs/0811.0909

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