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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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On the Law of the Iterated Logarithm
American Journal of Mathematics, 1941Hartman, Philip, Wintner, Aurel
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On the Law of the Iterated Logarithm
Journal of the London Mathematical Society, 1962Rogers, C. A., Taylor, S. J.
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On The Law of The Iterated Logarithm
1992We consider a sequence of independent random variables with zero expectations E zn .
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The law of the iterated logarithm in C[0,1]
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1976The law of the iterated logarithm is proved for C[0,1] valued random variables under conditions related to those used to establish the central limit theorem.
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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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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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A Theorem on the Law of the Iterated Logarithm
Theory of Probability & Its Applications, 1971openaire +1 more source
A law of the iterated logarithm under sublinear expectations
Journal of Financial Engineering, 2014Feng Hu, Zengjing Chen
exaly
The law of the iterated logarithm for discrepancies of {θ n x}
Acta Mathematica Hungarica, 2007Fukuyama K, K Fukuyama
exaly