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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The law of the iterated logarithm for LNQD sequences [PDF]
Journal of Inequalities and Applications, 2018 Let {ξi,i∈Z}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{\xi_{i},i ...
Yong Zhang
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A law of the iterated logarithm for Grenander's estimator. [PDF]
Stoch Process Their Appl, 2015 In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If $f(t_0) > 0$, $f'(t_0) < 0$, and $f'$ is continuous in a neighborhood of $t_0$, then \begin{eqnarray*} \limsup_{n ...
L. Dümbgen, J. Wellner, Malcolm Wolff
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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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Law of the iterated logarithm for some Markov operators [PDF]
Asymptotic Analysis, 2015 The law of the iterated logarithm for some Markov operators, which converge exponentially to the invariant measure, is established. The operators correspond to iterated function systems which, for example, may be used to generalize the cell cycle model ...
S. Hille +3 more
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A characterization of Chover-type law of iterated logarithm [PDF]
Springerplus, 2014 Let 0 < α ≤ 2 and − ∞
Deli Li, Pingyan Chen
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Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm [PDF]
, 2014 Kolmogorov’s exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables.
Li-Xin Zhang
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Self-Normalized Moderate Deviations for Degenerate U-Statistics [PDF]
EntropyIn this paper, we study self-normalized moderate deviations for degenerate U-statistics of order 2. Let {Xi,i≥1} be i.i.d. random variables and consider symmetric and degenerate kernel functions in the form h(x,y)=∑l=1∞λlgl(x)gl(y), where λl>0, Egl(X1)=0,
Lin Ge, Hailin Sang, Qi-Man Shao
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Invariance principles for the law of the iterated logarithm under G-framework
, 2015 The classical law of the iterated logarithm (LIL for short)as fundamental limit theorems in probability theory play an important role in the development of probability theory and its applications.
Panyu Wu, Zengjing Chen
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On the laws of the iterated logarithm under the sub-linear expectations without the assumption on the continuity of capacities [PDF]
Probability, Uncertainty and Quantitative Risk, 2021 In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed.
Li-Xin Zhang
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