| 次线性期望下弱负相关随机变量的性质及其强大数定律 |
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| 引用本文： | 陈晓燕,许晓明.次线性期望下弱负相关随机变量的性质及其强大数定律[J].应用概率统计,2019(1):63-72. |
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| 作者姓名： | 陈晓燕 许晓明 |
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| 作者单位： | 南京理工大学理学院;南京师范大学数学科学学院 |
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| 基金项目： | 国家自然科学基金项目(批准号:11501293);江苏省高等学校自然科学研究项目(批准号:17KJB110009);南京理工大学科研启动基金项目共同资助 |
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| 摘 要： | 强大数定律是非可加概率(或非线性期望)框架下的重要理论.目前己有许多有关非可加概率(或非线性期望)下独立同分布或负相关随机变量序列的强大数定律的研究文献.本文在非可加概率和次线性期望框架下,引入弱负相关随机变量的概念,并研究了弱负相关随机变量的有关性质.作为应用,本文还证明了弱负相关随机变量序列的强大数定律.
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| 关 键 词： | 弱负相关随机变量 次线性期望 非可加概率测度 强大数定律 |
The Properties and Strong Law of Large Numbers for Weakly Negatively Dependent Random Variables under Sublinear Expectations |
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| CHEN Xiaoyan,XU Xiaoming.The Properties and Strong Law of Large Numbers for Weakly Negatively Dependent Random Variables under Sublinear Expectations[J].Chinese Journal of Applied Probability and Statisties,2019(1):63-72. |
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| Authors: | CHEN Xiaoyan XU Xiaoming |
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| Institution: | (School of Science,Nanjing University of Science and Technology,Nanjing,210094,China;School of Mathematical Sciences,Nanjing Normal University,Nanjing,210023,China) |
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| Abstract: | Strong laws of large numbers play key role in nonadditive probability theory.Recently,there are many research papers about strong laws of large numbers for independently and identically distributed(or negatively dependent)random variables in the framework of nonadditive probabilities(or nonlinear expectations).This paper introduces a concept of weakly negatively dependent random variables and investigates the properties of such kind of random variables under a framework of nonadditive probabilities and sublinear expectations.A strong law of large numbers is also proved for weakly negatively dependent random variables under a kind of sublinear expectation as an application. |
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| Keywords: | weakly negatively dependent random variables sublinear expectation nonadditive probability strong law of large numbers |
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