Distribution of the brownian motion on its way to hitting zero

Pavel Chigansky; Fima C. Klebaner

doi:10.1214/ECP.v13-1432

Distribution of the brownian motion on its way to hitting zero

Pavel Chigansky
, Fima C. Klebaner

Department of Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

For the one-dimensional Brownian motion B = (B_t)_t≥0, started at x > 0, and the first hitting time τ = inf(t ≥ 0: B_t = 0), we find the probability density of B_uτ for a u ∈ (0,1), i.e. of the Brownian motion on its way to hitting zero.

Original language	English
Pages (from-to)	641-648
Number of pages	8
Journal	Electronic Communications in Probability
Volume	13
DOIs	https://doi.org/10.1214/ECP.v13-1432
State	Published - 1 Jan 2008

Keywords

Bessel bridge
Brownian bridge
Brownian motion
Heavy-tailed distribution
Hitting time
Scaled Brownian excursion

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10.1214/ECP.v13-1432

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title = "Distribution of the brownian motion on its way to hitting zero",

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 u ∈ (0,1), i.e. of the Brownian motion on its way to hitting zero.",

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N2 - 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 u ∈ (0,1), i.e. of the Brownian motion on its way to hitting zero.

AB - 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 u ∈ (0,1), i.e. of the Brownian motion on its way to hitting zero.

KW - Bessel bridge

KW - Brownian bridge

KW - Brownian motion

KW - Heavy-tailed distribution

KW - Hitting time

KW - Scaled Brownian excursion

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JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -

Distribution of the brownian motion on its way to hitting zero

Abstract

Keywords

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