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On the law of the iterated logarithm. I
Indagationes Mathematicae (Proceedings), 1955Die Verff. beweisen den folgenden Satz: Es sei \(n_1 < n_2 < \cdots\) eine unendliche Folge von positiven Zahlen mit \(n_{\nu+1}/n_\nu \geq q>1 \; (\nu =1,2,...)\). Für fast alle reellen \(x\) ist dann \(\limsup_{N \to \infty} (N \log\log N )^{-1/2} \left|\sum_{\nu=1}^N \exp 2 \pi i n_\nu x \right| =1\).
Erdős, Pál, Gál, István Sándor
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The law of the iterated logarithms
The science reports of the Kanazawa University＝金沢大学理科報告, 1961Not ...
Matsuyama, Noboru, Takahashi, Shigeru
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On the law of the iterated logarithm
The science reports of the Kanazawa University＝金沢大学理科報告, 1955Not ...
Matsuyama, Noboru, Takahashi, Shigeru
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On the Law of the Iterated Logarithm
The Annals of Mathematics, 1942Not ...
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The Limit Law of the Iterated Logarithm
Journal of Theoretical Probability, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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1994
Let the kernel Φ have the rank r = 1 and satisfy the conditions $$Eg_1^2 < \infty ,E|\Phi {|^{4/3}} < \infty $$ (9.1.1)
V. S. Koroljuk, Yu. V. Borovskich
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Let the kernel Φ have the rank r = 1 and satisfy the conditions $$Eg_1^2 < \infty ,E|\Phi {|^{4/3}} < \infty $$ (9.1.1)
V. S. Koroljuk, Yu. V. Borovskich
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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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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
2014The first law of the iterated logarithm is proved for symmetric Bernoulli random variables, that is, for independent ...
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