Electronic Communications in Probability

Distribution of the Brownian motion on its way to hitting zero

Pavel Chigansky and Fima Klebaner

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For the one-dimensional Brownian motion $B=(B_t)_{t\geq 0}$, started at $x<0$, and the  first hitting time $\tau=\inf\{t\geq 0:B_t=0\}$, we find the probability density of $B_{u\tau}$ for a $u\in$, i.e. of the Brownian motion on its way to hitting zero.

Article information

Electron. Commun. Probab., Volume 13 (2008), paper no. 58, 641-648.

Accepted: 17 December 2008
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65]

Brownian motion hitting time heavy-tailed distribution scaled Brownian excursion Bessel bridge Brownian bridge

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Chigansky, Pavel; Klebaner, Fima. Distribution of the Brownian motion on its way to hitting zero. Electron. Commun. Probab. 13 (2008), paper no. 58, 641--648. doi:10.1214/ECP.v13-1432. https://projecteuclid.org/euclid.ecp/1465233485

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