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Asymptotics for the Moment Convergence of U-Statistics in LIL
Journal of Inequalities and Applications, 2010 Let Un be a U-statistic based on a symmetric kernel h(x,y) and i.i.d. samples {X,Xn;n≥1}. In this paper, the exact moment convergence rates in the law of the iterated logarithm and the law of the logarithm of Un are obtained, which extend previous
Ke-Ang Fu
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One-Sided Version of Law of the Iterated Logarithm for Summations of Signum Functions
Journal of Mathematics, 2023 The law of the iterated logarithm (LIL), which describes the rate of convergence for a convergent lacunary series, was established by R. Salem and A. Zygmund.
Santosh Ghimire
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Zhejiang Daxue xuebao. Lixue ban, 2000 The aim of this paper is to establish a law of the iterated logarithm for non-stationary weakly negatively associated random vectors in under the finite second moment.
RUANHong-shun(阮宏顺) +2 more
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The law of the iterated logarithm for exchangeable random variables
International Journal of Mathematics and Mathematical Sciences, 1995 In this note, necessary and sufficient conditions for laws of the iterated logarithm are developed for exchangeable random variables.
Hu-Ming Zhang, Robert L. Taylor
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On Feller's criterion for the law of the iterated logarithm
International Journal of Mathematics and Mathematical Sciences, 1994 Combining Feller's criterion with a non-uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm.
Deli Li, M. Bhaskara Rao, Xiangchen Wang
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On the converse to the iterated logarithm law [PDF]
Journal of Applied Probability, 1968 Let Xi, i = 1, 2, 3,… be a sequence of independent and identically distributed random variables with law ℓ(X) and write. if EX = 0 and EX2 = σ2 < ∞, the law of the iterated logarithm (Hartman and Wintner [1]) tells us that
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Laws of the k-Iterated Logarithm of Weighted Sums in a Sub-Linear Expected Space
MathematicsThe law of the iterated logarithm precisely refines the law of large numbers and plays a fundamental role in probability limit theory. The framework of sub-linear expectation spaces substantially extends the classical concept of probability spaces.
Xiang Zeng
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The Other Law of the Iterated Logarithm
The Annals of Probability, 1975 Let $\{X_n\}$ be a sequence of independent, identically distributed random variables with $EX_1 = 0, EX_1^2 = 1$. Define $S_n = X_1 + \cdots + X_n$, and $A_n = \max_{1\leqq k\leqq n} |S_k|$. We prove that $\lim \inf A_n(n/\log \log n)^{-\frac{1}{2}} = \pi/8^{\frac{1}{2}}$ with probability one.
Jain, Naresh C., Pruitt, William E.
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The Law of the Iterated Logarithm
Journal of Institute of Science and Technology, 2022 The article begins first with the history and the development of the law of the iterated logarithm, abbreviated LIL. We then discuss the LIL in the context of independent random variables, dyadic martingales, lacunary trigonometric series, and harmonic functions. Finally, we derive a LIL for a sequence of dyadic martingales.
Santosh Ghimire, Hari Thapa
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A Law of the Iterated Logarithm for Sub-Linear Expectation Under a General Moment Condition
MathematicsIn this paper, we obtain the law of the iterated logarithm under a general moment condition with respect to sub-linear expectation. We present a novel proof by combining the exponential inequality with the subsequence method.
Xinrong Han, Cheng Hu
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