Sharp probability estimates for random walks with barriers

Kevin Ford

doi:10.1007/s00440-008-0168-4

Sharp probability estimates for random walks with barriers

Kevin Ford

Mathematics

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

Abstract

We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,∞) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided the fourth moment is finite.

Original language	English (US)
Pages (from-to)	269-283
Number of pages	15
Journal	Probability Theory and Related Fields
Volume	145
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-008-0168-4
State	Published - Sep 2009

Keywords

Ballot theorems
Barrier
Random walk

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

Online availability

10.1007/s00440-008-0168-4

Library availability

Discover UIUC Full Text

Cite this

@article{48e8e3c3db67429492e60abb45efef43,

title = "Sharp probability estimates for random walks with barriers",

abstract = "We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,∞) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided the fourth moment is finite.",

keywords = "Ballot theorems, Barrier, Random walk",

author = "Kevin Ford",

note = "The author was supported by NSF grants DMS-0301083 and DMS-0555367.",

year = "2009",

month = sep,

doi = "10.1007/s00440-008-0168-4",

language = "English (US)",

volume = "145",

pages = "269--283",

journal = "Probability Theory and Related Fields",

issn = "0178-8051",

publisher = "Springer New York",

number = "1-2",

}

TY - JOUR

T1 - Sharp probability estimates for random walks with barriers

AU - Ford, Kevin

N1 - The author was supported by NSF grants DMS-0301083 and DMS-0555367.

PY - 2009/9

Y1 - 2009/9

N2 - We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,∞) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided the fourth moment is finite.

AB - We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,∞) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided the fourth moment is finite.

KW - Ballot theorems

KW - Barrier

KW - Random walk

UR - https://www.scopus.com/pages/publications/67649133618

UR - https://www.scopus.com/pages/publications/67649133618#tab=citedBy

U2 - 10.1007/s00440-008-0168-4

DO - 10.1007/s00440-008-0168-4

M3 - Article

AN - SCOPUS:67649133618

SN - 0178-8051

VL - 145

SP - 269

EP - 283

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1-2

ER -

Sharp probability estimates for random walks with barriers

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this