The Law of the Iterated Logarithm for Linear Processes Generated by a Sequence of Stationary Independent Random Variables under the Sub-Linear Expectation [PDF]
Entropy, 2021 In this paper, we obtain the law of iterated logarithm for linear processes in sub-linear expectation space. It is established for strictly stationary independent random variable sequences with finite second-order moments in the sense of non-additive ...
Wei Liu, Yong Zhang
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One-Sided Version of Law of the Iterated Logarithm for Summations of Signum Functions [PDF]
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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A law of iterated logarithm for the subfractional Brownian motion and an application [PDF]
Journal of Inequalities and Applications, 2018 Let SH={StH,t≥0} $S^{H}=\{S^{H}_{t},t\geq0\}$ be a sub-fractional Brownian motion with Hurst index 00) $(x>0)$ with ΦH(0)=0 $\Phi_{H}(0)=0$.
Hongsheng Qi, Litan Yan
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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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General Law of iterated logarithm for Markov processes: Liminf laws [PDF]
Transactions of the American Mathematical Society. Series B, 2022 Continuing from Cho, Kim, and Lee [General Law of iterated logarithm for Markov processes: Limsup law, arXiv:2102,01917v3], in this paper, we discuss general criteria and forms of liminf laws of iterated logarithm (LIL) for continuous-time Markov ...
Soobin Cho, Panki Kim, Jaehun Lee
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Diophantine conditions in the law of the iterated logarithm for lacunary systems. [PDF]
Probab Theory Relat Fields, 2023 It is a classical observation that lacunary function systems exhibit many properties which are typical for systems of independent random variables. However, it had already been observed by Erdős and Fortet in the 1950s that probability theory’s limit ...
Aistleitner C, Frühwirth L, Prochno J.
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Iterated Law of Iterated Logarithm [PDF]
The Annals of Probability, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Burdzy, Krzysztof, San Martin, Jaime
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The law of the iterated logarithm for LNQD sequences [PDF]
Journal of Inequalities and Applications, 2018 Let { ξ i , i ∈ Z } $\{\xi_{i},i\in{\mathbb{Z}}\}$ be a stationary LNQD sequence of random variables with zero means and finite variance. In this paper, by the Kolmogorov type maximal inequality and Stein’s method, we establish the result of the law of ...
Yong Zhang
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Chover-Type Laws of the Iterated Logarithm for Kesten-Spitzer Random Walks in Random Sceneries Belonging to the Domain of Stable Attraction [PDF]
Discrete Dynamics in Nature and Society, 2018 Let X={Xi,i≥1} be a sequence of real valued random variables, S0=0 and Sk=∑i=1kXi (k≥1). Let σ={σ(x),x∈Z} be a sequence of real valued random variables which are independent of X’s.
Wensheng Wang, Anwei Zhu
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A Generalization of Kolmogorov's Law of the Iterated Logarithm [PDF]
Proceedings of the American Mathematical Society, 1972 A version of the law of the iterated logarithm is proved for sequences of independent random variables which satisfy the central limit theorem in such a way that the convergence of the appropriate moment-generating functions to that of the standard normal distribution occurs at a particular rate.
R. J. Tomkins
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