scholarly journals On the law of the iterated logarithm for continued fractions with sequentially restricted partial quotients

Nonlinearity ◽  
2021 ◽  
Vol 34 (3) ◽  
pp. 1389-1407
Author(s):  
Manuel Stadlbauer ◽  
Xuan Zhang
Keyword(s):  
Continued Fractions ◽  
Iterated Logarithm ◽  
Partial Quotients ◽  
The Law

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

scholarly journals Continued fractions with low complexity: transcendence measures and quadratic approximation

2012 ◽  
Vol 148 (3) ◽  
pp. 718-750 ◽  
Author(s):  
Yann Bugeaud
Keyword(s):  
Lower Bound ◽  
Continued Fractions ◽  
Low Complexity ◽  
Quadratic Approximation ◽  
Real Numbers ◽  
Partial Quotients ◽  
Block Complexity

AbstractWe establish measures of non-quadraticity and transcendence measures for real numbers whose sequence of partial quotients has sublinear block complexity. The main new ingredient is an improvement of Liouville’s inequality giving a lower bound for the distance between two distinct quadratic real numbers. Furthermore, we discuss the gap between Mahler’s exponent w2 and Koksma’s exponent w*2.

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
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