On the distribution of the Brownian motion process on its way to hitting zero

Details On the distribution of the Brownian motion process on its way to hitting zero On the distribution of the Brownian motion process on its way to hitting zero

2010-01-05

arxiv.org/abs/1001.0628v2

Mathematics

Probability

5 pages, 0 figures

Scientific paper

We present functional versions of recent results on the univariate
distributions of the process $V_{x,u} = x + W_{u\tau(x)},$ $0\le u\le 1$, where
$W_\bullet$ is the standard Brownian motion process, $x>0$ and $\tau (x)
=\inf\{t>0 : W_{t}=-x\}$.

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