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Parameter-Dependent Law of the Iterated Logarithm

Theory of Probability & Its Applications, 1988
See the review in Zbl 0623.60043.
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Law of the Iterated Logarithm

2014
For sums of independent random variables we already know two limit theorems: the law of large numbers and the central limit theorem. The law of large numbers describes for large \(n\in \mathbb{N}\) the typical behavior, or average value behavior, of sums of n random variables.
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Bearing fault diagnosis via generalized logarithm sparse regularization

Mechanical Systems and Signal Processing, 2022
Weiguo Huang, Zeshu Song, Juanjuan Shi
exaly  

The Law of the Iterated Logarithm

2014
The first law of the iterated logarithm is proved for symmetric Bernoulli random variables, that is, for independent ...
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The Law of the Iterated Logarithm

1975
In this chapter we shall consider a sequence of independent random variables X n ; n = 1, 2, ... with zero means and finite variances.
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The Law of the Iterated Logarithm

2012
The central limit theorem tells us that suitably normalized sums can be approximated by a normal distribution. Although arbitrarily large values may occur, and will occur, one might try to bound the magnitude in some manner. This is what the law of the iterated logarithm (LIL) does, in that it provides a parabolic bound on how large the oscillations of
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Series Involving Iterated Logarithms

The College Mathematics Journal, 2009
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