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Distribution of the Brownian motion on its way to hitting zero
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Pavel Chigansky, The Hebrew University
Fima C. Klebaner, Monash University
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Abstract
For the one-dimensional Brownian motion $B=(Bt)t≥
0$, started at $x>0$, and the first hitting time
$τ=inf{t≥ 0:Bt=0}$, we find the probability density of
$Buτ$ for a $uin(0,1)$, i.e. of the Brownian motion on its way
to hitting zero.
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Full text: PDF
Pages: 641-648
Published on: December 17, 2008
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Electronic Communications in Probability. ISSN: 1083-589X |
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