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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 quenched limiting distributions of a one-dimensional random walk in random scenery
, 2013 For a one-dimensional random walk in random scenery (RWRS) on Z, we determine its quenched weak limits by applying Strassen's functional law of the iterated logarithm. As a consequence, conditioned on the random scenery, the one-dimensional RWRS does not
Guillotin-Plantard, Nadine +2 more
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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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Oscillation of generalized differences of H\"older and Zygmund functions
, 2016 In this paper we analyze the oscillation of functions having derivatives in the H\"older or Zygmund class in terms of generalized differences and prove that its growth is governed by a version of the classical Kolmogorov's Law of the Iterated Logarithm ...
Castro, Alejandro J. +2 more
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On The Law of the Iterated Logarithm in Hybrid Multiphase Queueing Systems
Operations Research and Decisions, 2020 The model of a hybrid multiphase queueing system (HMQS) has been developed to measure the performance of complex computer networks working under conditions of heavy traffic.
Saulius Minkevičius
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Limiting behavior of delayed sums under a non-identically distribution setup
Anais da Academia Brasileira de Ciências, 2008 We present an accurate description the limiting behavior of delayed sums under a non-identically distribution setup, and deduce Chover-type laws of the iterated logarithm for them.
Chen Pingyan
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Journal of Inequalities and Applications, 2016 We assume that X k = ∑ i = − ∞ + ∞ a i ξ i + k $X_{k}=\sum_{i=-\infty}^{+\infty}a_{i}\xi_{i+k}$ is a moving average process and { ξ i , − ∞ < i < + ∞ } $\{\xi_{i},-\infty ...
Yayun Zhang, Qunying Wu
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Kolmogorov's law of the iterated logarithm for noncommutative martingales
, 2014 We prove Kolmogorov's law of the iterated logarithm for noncommutative martingales. The commutative case was due to Stout.
Zeng, Qiang
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Planar mappings of subexponentially integrable distortion -- integrability of distortion of inverses
, 2016 We establish the optimal regularity for the distortion of inverses of mappings of finite distortion with logarithm-iterated style subexponentially integrable distortion, which generalizes the Theorem 1. of [J. Gill, Ann. Acad. Sci. Fenn. Math. 35 (2010),
Xu, Haiqing
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Some Probability Inequalities for Quadratic Forms of Negatively Dependent Subgaussian Random Variables [PDF]
Journal of Sciences, Islamic Republic of Iran, 2005 In this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables.
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