On the uniqueness of the maximum of the paths of random walks

Manfred Heinz Denker, Susanne Koch

Research output: Contribution to journalArticle

Abstract

Let ξi be i.i.d. symmetric random variables with P (ξi = 1) = frac(1, 2) and denote by Sn their partial sums. We derive the distribution of the difference in the position of the last and first maximum of the random walk Sn up to time t.

Original languageEnglish (US)
Pages (from-to)659-668
Number of pages10
JournalJournal of Statistical Planning and Inference
Volume137
Issue number3
DOIs
StatePublished - Mar 1 2007

Fingerprint

Partial Sums
Random variables
Random walk
Uniqueness
Random variable
Denote
Path

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Denker, Manfred Heinz ; Koch, Susanne. / On the uniqueness of the maximum of the paths of random walks. In: Journal of Statistical Planning and Inference. 2007 ; Vol. 137, No. 3. pp. 659-668.
@article{bd57f7a96ca145c1be40f73cc0fb6aaa,
title = "On the uniqueness of the maximum of the paths of random walks",
abstract = "Let ξi be i.i.d. symmetric random variables with P (ξi = 1) = frac(1, 2) and denote by Sn their partial sums. We derive the distribution of the difference in the position of the last and first maximum of the random walk Sn up to time t.",
author = "Denker, {Manfred Heinz} and Susanne Koch",
year = "2007",
month = "3",
day = "1",
doi = "10.1016/j.jspi.2006.06.028",
language = "English (US)",
volume = "137",
pages = "659--668",
journal = "Journal of Statistical Planning and Inference",
issn = "0378-3758",
publisher = "Elsevier",
number = "3",

}

On the uniqueness of the maximum of the paths of random walks. / Denker, Manfred Heinz; Koch, Susanne.

In: Journal of Statistical Planning and Inference, Vol. 137, No. 3, 01.03.2007, p. 659-668.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the uniqueness of the maximum of the paths of random walks

AU - Denker, Manfred Heinz

AU - Koch, Susanne

PY - 2007/3/1

Y1 - 2007/3/1

N2 - Let ξi be i.i.d. symmetric random variables with P (ξi = 1) = frac(1, 2) and denote by Sn their partial sums. We derive the distribution of the difference in the position of the last and first maximum of the random walk Sn up to time t.

AB - Let ξi be i.i.d. symmetric random variables with P (ξi = 1) = frac(1, 2) and denote by Sn their partial sums. We derive the distribution of the difference in the position of the last and first maximum of the random walk Sn up to time t.

UR - http://www.scopus.com/inward/record.url?scp=33750516525&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750516525&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2006.06.028

DO - 10.1016/j.jspi.2006.06.028

M3 - Article

AN - SCOPUS:33750516525

VL - 137

SP - 659

EP - 668

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 3

ER -