Electronic Communications in Probability

Distribution of the Brownian motion on its way to hitting zero

Pavel Chigansky and Fima Klebaner

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465233485

Digital Object Identifier
doi:10.1214/ECP.v13-1432

Mathematical Reviews number (MathSciNet)
MR2466191

Zentralblatt MATH identifier
1189.60146

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

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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