Distribution of the Brownian motion on its way to hitting zero

Details Distribution of the Brownian motion on its way to hitting zero Distribution of the Brownian motion on its way to hitting zero

2008-11-06

arxiv.org/abs/0811.0909v2

Elect. Comm. in Probab., 13(2008), pp. 641-648

Mathematics

Probability

7 pages, final version

Scientific paper

For the one-dimensional Brownian motion $B=(B_t)_{t\ge 0}$, started at $x>0$,
and the first hitting time $\tau=\inf\{t\ge 0:B_t=0\}$, 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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