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On the laws of the iterated logarithm under sub-linear expectations

Probability, Uncertainty and Quantitative Risk 2021年第4期6卷 409-460页

作者： Li-Xin Zhang School of Mathematical Sciences Zhejiang UniversityHangzhou 310027ZhejiangChina

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 *** inequalities for the maximum sum of independent random variables and Kolmogorov’s converse exponential inequalities are established as tools for showing the law of the iterated *** an application,the sufficient and necessary conditions of the law of the iterated logarithm for independent and identically distributed random variables under the sub-linear expectation are *** the paper,it is also shown that if the sub-linear expectation space is rich enough,it will have no continuous *** laws of the iterated logarithm are established without the assumption on the continuity of capacities.

关键词： Sub-linear expectation Capacity Kolmogorov’s exponential inequality laws of the iterated logarithm

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STRONG LIMIT THEOREMS FOR EXTENDED INDEPENDENT RANDOM VARIABLES AND EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS

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Acta Mathematica Scientia 2022年第2期42卷 467-490页

作者： Li-Xin ZHANG School of Mathematical Sciences Zhejiang UniversityHangzhou 310027China

Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have attracted a lot of interest *** purpose of this paper is to study the strong law of large numbers and the law of the iterated logarithm for a sequence of random variables in a sub-linear expectation space under a concept of extended independence which is much weaker and easier to verify than the independence proposed by Peng[20].We introduce a concept of extended negative dependence which is an extension of the kind of weak independence and the extended negative independence relative to classical probability that has appeared in the recent *** tools such as moment inequality and Kolmogorov’s exponential inequality are established for these kinds of extended negatively independent random variables,and these tools improve a lot upon those of Chen,Chen and Ng[1].The strong law of large numbers and the law of iterated logarithm are also obtained by applying these inequalities.

关键词： Sub-linear expectation capacity extended negative dependence Kolmogorov’s exponential inequality laws of the iterated logarithm law of large numbers

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Limiting Behavior of Delayed Sums of φ-Mixing under a Non-Identical Distribution Setup

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Journal of Mathematical Research and Exposition 2008年第3期28卷 628-636页

作者： CHEN Ping Yan LI Feng Ling Department of Mathematics Jinan University Guangdong 510630 China Department of Statistics Jinan University Guangdong 510630 China

We present an integral test to determine the limiting behavior of delayed sums under a non-identical distribution setup for φ-mixing sequence, and deduce Chover-type laws of the iterated logarithm for them. These com... 详细信息

关键词： stable distribution laws of the iterated logarithm delayed sum integral test

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