scholarly journals Metric discrepancy results for Erdős-Fortet sequence

2012 ◽  
Vol 49 (1) ◽  
pp. 52-78 ◽  
Author(s):  
Katusi Fukuyama ◽  
Sho Miyamoto
Keyword(s):  
Iterated Logarithm ◽  
The Law ◽  
Star Discrepancy

For the classical Erdős-Fortet sequence nk = 2k − 1 we show that the law of the iterated logarithm for star discrepancy of {nkx} has non-constant limsup, while the law for discrepancy has constant limsup.

scholarly journals The Law of the Iterated Logarithm for a Markov Process

1970 ◽  
Vol 41 (3) ◽  
pp. 945-955 ◽  
Author(s):  
R. P. Pakshirajan ◽  
M. Sreehari
Keyword(s):  
Markov Process ◽  
Iterated Logarithm ◽  
The Law

Extreme values and the law of the iterated logarithm

1987 ◽  
Vol 74 (3) ◽  
pp. 319-340 ◽  
Author(s):  
J. Kuelbs ◽  
M. Ledoux
Keyword(s):  
Extreme Values ◽  
Iterated Logarithm ◽  
The Law

The law of the Iterated Logarithm for random interval homeomorphisms

2021 ◽  
Author(s):  
Klaudiusz Czudek ◽  
Tomasz Szarek ◽  
Hanna Wojewódka-Ściążko
Keyword(s):  
Random Interval ◽  
Iterated Logarithm ◽  
The Law

On the Limit Set in the Law of the Iterated Logarithm for U-statistics of Order Two

2004 ◽  
pp. 111-126
Author(s):  
Stanislaw Kwapień ◽  
Rafał Latała ◽  
Krzysztof Oleszkiewicz ◽  
Joel Zinn
Keyword(s):  
Limit Set ◽  
U Statistics ◽  
Iterated Logarithm ◽  
The Law

scholarly journals On the law of the iterated logarithm in the infinite variance case

1980 ◽  
Vol 30 (1) ◽  
pp. 5-14 ◽  
Author(s):  
R. A. Maller
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Infinite Variance ◽  
Iterated Logarithm ◽  
The Law ◽  
Necessary And Sufficient ◽  
Independent And Identically Distributed

AbstractThe main purpose of the paper is to give necessary and sufficient conditions for the almost sure boundedness of (Sn – αn)/B(n), where Sn = X1 + X2 + … + XmXi being independent and identically distributed random variables, and αnand B(n) being centering and norming constants. The conditions take the form of the convergence or divergence of a series of a geometric subsequence of the sequence P(Sn − αn > a B(n)), where a is a constant. The theorem is distinguished from previous similar results by the comparative weakness of the subsidiary conditions and the simplicity of the calculations. As an application, a law of the iterated logarithm general enough to include a result of Feller is derived.

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