Standard

Strong laws for the maximal gain over increasing runs. / Frolov, Andrei; Martikainen, Alexander; Steinebach, Josef.

в: Statistics and Probability Letters, Том 50, № 3, 15.11.2000, стр. 305-312.

Результаты исследований: Научные публикации в периодических изданияхстатьяРецензирование

Harvard

Frolov, A, Martikainen, A & Steinebach, J 2000, 'Strong laws for the maximal gain over increasing runs', Statistics and Probability Letters, Том. 50, № 3, стр. 305-312. https://doi.org/10.1016/s0167-7152(00)00119-x

APA

Frolov, A., Martikainen, A., & Steinebach, J. (2000). Strong laws for the maximal gain over increasing runs. Statistics and Probability Letters, 50(3), 305-312. https://doi.org/10.1016/s0167-7152(00)00119-x

Vancouver

Frolov A, Martikainen A, Steinebach J. Strong laws for the maximal gain over increasing runs. Statistics and Probability Letters. 2000 Нояб. 15;50(3):305-312. https://doi.org/10.1016/s0167-7152(00)00119-x

Author

Frolov, Andrei ; Martikainen, Alexander ; Steinebach, Josef. / Strong laws for the maximal gain over increasing runs. в: Statistics and Probability Letters. 2000 ; Том 50, № 3. стр. 305-312.

BibTeX

@article{4834df4639c845f7b1fe0459103becfd,
title = "Strong laws for the maximal gain over increasing runs",
abstract = "Let {(Xi,Yi)}i=1,2,... be an i.i.d. sequence of bivariate random vectors with P(Y1=y)=0 for all y. Put Mn=Mn(Ln)=max0≤k≤n-Ln(X k+1++Xk+Ln)Ik,Ln, where Ik,ℓ=I{Yk+1≤≤Yk+ℓ} denotes the indicator function of the event in brackets, Ln is the largest ℓ≤n, for which Ik,ℓ=1 for some k=0,1,...,n-ℓ. If, for example, Xi=Yi, i≥1, and Xi denotes the gain in the ith repetition of a game of chance, then Mn is the maximal gain over increasing runs of maximal length Ln. We derive a strong law of large numbers and a law of iterated logarithm type result for Mn.",
keywords = "Increasing run, Law of iterated logarithm, Primary 60F15, Secondary 60F10, Strong law of large numbers",
author = "Andrei Frolov and Alexander Martikainen and Josef Steinebach",
note = "Funding Information: This research was started when the first two authors visited Marburg. They gratefully acknowledge partial support by a special research grant from the University of Marburg, which made this exchange possible, and by grant 96-01-00547 from RFBR. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2000",
month = nov,
day = "15",
doi = "10.1016/s0167-7152(00)00119-x",
language = "English",
volume = "50",
pages = "305--312",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier",
number = "3",

}

RIS

TY - JOUR

T1 - Strong laws for the maximal gain over increasing runs

AU - Frolov, Andrei

AU - Martikainen, Alexander

AU - Steinebach, Josef

N1 - Funding Information: This research was started when the first two authors visited Marburg. They gratefully acknowledge partial support by a special research grant from the University of Marburg, which made this exchange possible, and by grant 96-01-00547 from RFBR. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2000/11/15

Y1 - 2000/11/15

N2 - Let {(Xi,Yi)}i=1,2,... be an i.i.d. sequence of bivariate random vectors with P(Y1=y)=0 for all y. Put Mn=Mn(Ln)=max0≤k≤n-Ln(X k+1++Xk+Ln)Ik,Ln, where Ik,ℓ=I{Yk+1≤≤Yk+ℓ} denotes the indicator function of the event in brackets, Ln is the largest ℓ≤n, for which Ik,ℓ=1 for some k=0,1,...,n-ℓ. If, for example, Xi=Yi, i≥1, and Xi denotes the gain in the ith repetition of a game of chance, then Mn is the maximal gain over increasing runs of maximal length Ln. We derive a strong law of large numbers and a law of iterated logarithm type result for Mn.

AB - Let {(Xi,Yi)}i=1,2,... be an i.i.d. sequence of bivariate random vectors with P(Y1=y)=0 for all y. Put Mn=Mn(Ln)=max0≤k≤n-Ln(X k+1++Xk+Ln)Ik,Ln, where Ik,ℓ=I{Yk+1≤≤Yk+ℓ} denotes the indicator function of the event in brackets, Ln is the largest ℓ≤n, for which Ik,ℓ=1 for some k=0,1,...,n-ℓ. If, for example, Xi=Yi, i≥1, and Xi denotes the gain in the ith repetition of a game of chance, then Mn is the maximal gain over increasing runs of maximal length Ln. We derive a strong law of large numbers and a law of iterated logarithm type result for Mn.

KW - Increasing run

KW - Law of iterated logarithm

KW - Primary 60F15

KW - Secondary 60F10

KW - Strong law of large numbers

UR - http://www.scopus.com/inward/record.url?scp=0013313834&partnerID=8YFLogxK

U2 - 10.1016/s0167-7152(00)00119-x

DO - 10.1016/s0167-7152(00)00119-x

M3 - Article

AN - SCOPUS:0013313834

VL - 50

SP - 305

EP - 312

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 3

ER -

ID: 75020743