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

Access to Document

10.1214/ECP.v13-1432

Cite this

@article{235d09a2352b4a6baf95b51f7283ad1f,

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.",

keywords = "Bessel bridge, Brownian bridge, Brownian motion, Heavy-tailed distribution, Hitting time, Scaled Brownian excursion",

author = "Pavel Chigansky and Klebaner, {Fima C.}",

year = "2008",

month = jan,

day = "1",

doi = "10.1214/ECP.v13-1432",

language = "אנגלית",

volume = "13",

pages = "641--648",

journal = "Electronic Communications in Probability",

issn = "1083-589X",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - Distribution of the brownian motion on its way to hitting zero

AU - Chigansky, Pavel

AU - Klebaner, Fima C.

PY - 2008/1/1

Y1 - 2008/1/1

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

UR - http://www.scopus.com/inward/record.url?scp=58149144597&partnerID=8YFLogxK

U2 - 10.1214/ECP.v13-1432

DO - 10.1214/ECP.v13-1432

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:58149144597

SN - 1083-589X

VL - 13

SP - 641

EP - 648

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

ER -

Distribution of the brownian motion on its way to hitting zero

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this