Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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 изданиях › статья › Рецензирование
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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