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The Law of the Iterated Logarithm
1991This chapter is devoted to the classical laws of the iterated logarithm of Kolmogorov and Hartman-Wintner-Strassen in the vector valued setting. These extensions both enlighten the scalar statements and describe various new interesting phenomena in the infinite dimensional setting.
Michel Ledoux, Michel Talagrand
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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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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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Variants on the Law of the Iterated Logarithm
Bulletin of the London Mathematical Society, 1986This is a review article surveying the numerous results of recent years related to the classical law of the iterated logarithm with particular reference to developments in the decade or so since the survey in Chapter 5 of the book by \textit{W. Stout}, Almost sure convergence (1974; Zbl 0321.60021).
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The Law of the Iterated Logarithm
2014The 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
1975In 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
2012The 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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The law of the iterated logarithm
2013For B, a standard BMP, we showed in Sec. (5.9) that wp1 \(\frac{{B\left( t \right)}} {t}\mathop { \to 0}\limits^{wp1}\), as t → ∞, that \(\overline {\mathop {\lim }\limits_{t \to \infty } } \frac{{B(t)}} {{\sqrt t }} = \infty\) and \(\mathop {\underline {\lim } }\limits_{t \to \infty } \frac{{B(t)}} {{\sqrt t }} = - \infty\).
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The law of iterated logarithm for logarithmic combinatorial assemblies
Lithuanian Mathematical Journal, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Bearing fault diagnosis via generalized logarithm sparse regularization
Mechanical Systems and Signal Processing, 2022Weiguo Huang, Zeshu Song, Juanjuan Shi
exaly
On the Law of the Iterated Logarithm
Journal of the London Mathematical Society, 1962Rogers, C. A., Taylor, S. J.
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