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

Konstantin Borovkov (University of Melbourne)

Abstract


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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Pages: 281-285

Publication Date: July 8, 2010

DOI: 10.1214/ECP.v15-1555

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