Results 21 to 30 of about 564 (258)
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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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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The law of iterated logarithm for the estimations of diffusion-type processes
Advances in Difference Equations, 2020 This paper mainly discusses the asymptotic behaviours on the lasso-type estimators for diffusion-type processes with a small noise. By constructing the objective function on the estimation, in view of convexity argument, it is proved that the estimator ...
Mingzhi Mao, Gang Huang
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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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Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective In multiple sclerosis, the optimal time for deploying a therapeutic intervention is before the central nervous system is damaged; given the success of trials treating the earliest stage of MS, the radiologically isolated syndrome, developing primary prevention strategies is an important next challenge.
Amy W. Laitinen +7 more
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Precise Asymptotics in the Law of Iterated Logarithm for Moving Average Process under Dependence
Journal of Inequalities and Applications, 2011 Let be a doubly infinite sequence of identically distributed and -mixing random variables, and let be an absolutely summable sequence of real numbers.
Jie Li
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Natural Frequencies of Levodopa‐Induced Dyskinesia in Parkinson's Disease
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objectives Abnormal involuntary movements, known as dyskinesias, are common complications of levodopa treatment in patients with Parkinson's disease and can significantly impair quality of life. The underlying pathophysiology remains unclear, and current therapeutic options are limited.
Ioannis U. Isaias +3 more
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