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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Central limit theorems for sub-linear expectation under the Lindeberg condition [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we investigate the central limit theorems for sub-linear expectation for a sequence of independent random variables without assumption of identical distribution. We first give a bound on the distance between the normalized sum distribution
Cheng Hu
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Moderate Deviation Principle for Linear Processes Generated by Dependent Sequences under Sub-Linear Expectation [PDF]
Axioms, 2023 We are interested in the linear processes generated by dependent sequences under sub-linear expectation. Using the Beveridge–Nelson decomposition of linear processes and the inequalities, the moderate deviation principle for linear processes produced by ...
Peiyu Sun +4 more
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Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables under sub-linear expectation [PDF]
Journal of Inequalities and Applications, 2017 In this paper, we study the complete convergence and complete moment convergence for weighted sums of extended negatively dependent (END) random variables under sub-linear expectations space with the condition of C V [ | X | p l ( | X | 1 / α ) ] < ∞ $C_{
Haoyuan Zhong, Qunying Wu
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Laws of the k-Iterated Logarithm of Weighted Sums in a Sub-Linear Expected Space [PDF]
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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On the laws of the iterated logarithm under sub-linear expectations
Probability, Uncertainty and Quantitative Risk, 2021 <p style='text-indent:20px;'>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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Moderate deviation principle for $ m $-dependent random variables under the sub-linear expectation
AIMS Mathematics, 2022 <abstract><p>Let $ \{X_n, n\geq1\} $ be a sequence of $ m $-dependent strictly stationary random variables in a sub-linear expectation $ (\Omega, \mathcal{H}, \mathbb{E}) $. In this article, we give the definition of $ m $-dependent sequence of random variables under sub-linear expectation spaces taking values in $ \mathbb{R} $.
Shuang Guo, Yong Zhang
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Three Series Theorem for Independent Random Variables under Sub-linear Expectations with Applications [PDF]
Acta Mathematica Sinica, English Series, 2018 In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we give a theorem about the convergence of a random series and establish a three series theorem of independent random variables under the sub-linear expectations.
Xu, Jia Pan, Zhang, Li Xin
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Donsker’s Invariance Principle Under the Sub-linear Expectation with an Application to Chung’s Law of the Iterated Logarithm [PDF]
Communications in Mathematics and Statistics, 2015 We prove a new Donsker's invariance principle for independent and identically distributed random variables under the sub-linear expectation. As applications, the small deviations and Chung's law of the iterated logarithm are obtained.
Li-Xin Zhang, Zhang Li-Xin
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Acta Mathematica Sinica, English Series, 2023 In this paper, by establishing a Borel-Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of independent random variables under the sub-linear expectation and a sequence of independent random variables on $\mathbb R^{\infty}$ under a probability, we give the sufficient and necessary conditions of the strong
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