Distribution of the Brownian motion on its way to hitting zero
Abstract
Description
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.
7 pages, final version
7 pages, final version