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Complete q-Order Moment Convergence of Moving Average Processes Generated by Negatively Dependent Random Variables under Sub-Linear Expectations 认领 引用
1
作者 Mingzhou XU 《Journal of Mathematical Research with Applications》 CSCD 2025年第3期395-410,共16页
Assume that{ai,−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{Xn=Σi=−∞∞aiY_(i+... Assume that{ai,−∞<i<∞}is an absolutely summable sequence of real numbers.We establish the complete q-order moment convergence for the partial sums of moving average processes{Xn=Σi=−∞∞aiYi+n,n≥1}under some proper conditions,where{Yi,-∞<i<∞}is a doubly infinite sequence of negatively dependent random variables under sub-linear expectations.These results extend and complement the relevant results in probability space. 展开更多
关键词 moving average processes negatively dependent random variables complete moment convergence sub-linear expectations
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STRONG LIMIT THEOREMS FOR EXTENDED INDEPENDENT RANDOM VARIABLES AND EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS 认领 引用 被引量：15
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作者 Li-Xin ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第2期467-490,共24页
Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have attracted a lot of interest recently.The purpose of this paper is to study the strong law of large numbers and... Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have attracted a lot of interest recently.The 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 literature.Powerful 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. 展开更多
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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Complete moment convergence for ND random variables under the sub-linear expectations 认领 引用
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作者 FENG Feng-xiang WANG Ding-cheng WU Qun-ying 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第3期444-457,共14页
In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of r... In this article,we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND)random variables under the sub-linear expectations.As applications,we can obtain a series of results on complete moment convergence for ND random variables under the sub-linear expectations. 展开更多
关键词 complete convergence complete moment convergence ND random variables sub-linear expectation
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Central limit theolrem for linear processes generated byⅡD random variables under the sub-linear expectation 认领 引用 被引量：2
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作者 LIU Wei ZHANG Yong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2021年第2期243-255,共13页
In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expec... In this paper,we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID)random variables for sub-linear expectations initiated by Peng[19].It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive. 展开更多
关键词 central limit theorem invariance principle ⅡD random variables sub-linear expectation linear process
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Sample Path Large Deviations for Independent Random Variables under Sub-Linear Expectations 认领 引用 被引量：1
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作者 Mingzhou XU 《Journal of Mathematical Research with Applications》 CSCD 2024年第4期541-550,共10页
In this work, the sample path large deviations for independent, identically distributed random variables under sub-linear expectations are established. The results obtained in sublinear expectation spaces extend the c... In this work, the sample path large deviations for independent, identically distributed random variables under sub-linear expectations are established. The results obtained in sublinear expectation spaces extend the corresponding ones in probability space. 展开更多
关键词 sample path large deviations independent random variables sub-linear expectation
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Large Deviations for the LS Estimator in Nonlinear Regression Model under Sub-linear Expectations 认领 引用
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作者 Yi WU Xue-jun WANG Li-xin ZHANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2026年第2期474-488,共15页
In this paper,we investigate some asymptotic properties of the least squares estimator in nonlinear regression model with independent and identically distributed random errors under sub-linear expectations.The large d... In this paper,we investigate some asymptotic properties of the least squares estimator in nonlinear regression model with independent and identically distributed random errors under sub-linear expectations.The large deviation results for the estimator are established under some general conditions.As applications,the results on weak consistency and strong consistency are obtained under the meaning of capacity.A simulation study is also presented to verify the validity of the theoretical results. 展开更多
关键词 least squares estimator nonlinear regression model sub-linear expectation large deviation consistency
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General Results on Strong Laws for Weighted Sums Under Sub-linear Expectations with a Statistical Application 认领 引用
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作者 Yi WU Mengmei XI Xuejun WANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2026年第3期491-510,共20页
In this paper,the authors investigate the double-indexed version of the strong law of large numbers under some general conditions in a sub-linear expectation space.The weighted version of the Marcinkiewicz-Zygmund typ... In this paper,the authors investigate the double-indexed version of the strong law of large numbers under some general conditions in a sub-linear expectation space.The weighted version of the Marcinkiewicz-Zygmund type strong law of large numbers is also established.These results extend or improve some existing ones in the classical probability space or a sub-linear expectation space.As an application,they further study the nonparametric regression model under the sub-linear expectation framework.Some numerical simulations are also presented. 展开更多
关键词 Strong law of large numbers Sub-linear expectations Nonparametric regression Numerical simulation
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Complete Moment Convergence for Arrays of Rowwise Negatively Dependent Random Variables under Sub-linear Expectations 认领 引用
8
作者 Miao-miao WANG Xue-jun WANG Hai-wu HUANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2026年第3期766-779,共14页
In this paper,under the condition that the Choquet expectations exist,we study the complete moment convergence for weighted sums of arrays of rowwise negatively dependent random variables in sublinear expectation spac... In this paper,under the condition that the Choquet expectations exist,we study the complete moment convergence for weighted sums of arrays of rowwise negatively dependent random variables in sublinear expectation space(Ω,H,E).Some general results on complete moment convergence for weighted sums of arrays of rowwise negatively dependent random variables under sub-linear expectations are established,which extend and improve some previous known ones. 展开更多
关键词 negatively dependent random variables complete moment convergence sub-linear expectation space capacity
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Strong Convergence Theorems Under Sub-linear Expectations and Its Applications in Nonparametric Regression Models 认领 引用
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作者 Yi Wu Xin Deng +1 位作者 Mengmei Xi Xuejun Wang 《Communications in Mathematics and Statistics》 SCIE CSCD 2025年第4期863-889,共27页
In this paper,we first study the complete convergence for arrays of rowwise widely orthant dependent random variables under sub-linear expectations.The complete convergence theorems are established in sense of sub-add... In this paper,we first study the complete convergence for arrays of rowwise widely orthant dependent random variables under sub-linear expectations.The complete convergence theorems are established in sense of sub-additive capacities under some mild conditions.As an application of the main results,we investigate the strong consistency for the weighted estimator in a nonparametric regression model based on widely orthant dependent errors under sub-linear expectations.In addition,we also obtain the rate of strong consistency for the estimator in a nonparametric regression model based on widely orthant dependent errors under sub-linear expectations. 展开更多
关键词 Complete convergence Capacity Sub-linear expectations Widely orthant dependent random variables Strong consistency
Strassen’s Law of the Iterated Logarithm under Sub-linear Expectations 认领 引用
10
作者 Wangyun Gu Lixin Zhang 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2025年第3期827-846,共20页
We establish the Strassen's law of the iterated logarithm(LIL for short)for independent and identically distributed random variables with E[X1]=ε[X1]=0 and Cv[X12]<∞ under a sublinear expectation ... We establish the Strassen's law of the iterated logarithm(LIL for short)for independent and identically distributed random variables with E[X1]=ε[X1]=0 and Cv[X12]<∞ under a sublinear expectation space with a countably sub-additive capacity V.We also show the LIL for upper capacity with σ=σ under some certain conditions. 展开更多
关键词 Sub-linear expectation capacity Strassen’s law of the iterated logarithm
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Three Series Theorem for Independent Random Variables under Sub-linear Expectations with Applications 认领 引用 被引量：9
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作者 Jia Pan XU Li Xin ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2019年第2期172-184,共13页
In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables ... In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz's strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive. 展开更多
关键词 Sub-linear expectation capacity Rosenthal's inequality Kolmogorov's three series theorem Marcinkiewicz's strong law of large numbers
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The Law of Logarithm for Arrays of Random Variables under Sub-linear Expectations 认领 引用 被引量：4
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作者 Jia-pan XU Li-xin ZHANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2020年第3期670-688,共19页
Under the framework of sub-linear expectation initiated by Peng,motivated by the concept of extended negative dependence,we establish a law of logarithm for arrays of row-wise extended negatively dependent random vari... Under the framework of sub-linear expectation initiated by Peng,motivated by the concept of extended negative dependence,we establish a law of logarithm for arrays of row-wise extended negatively dependent random variables under weak conditions.Besides,the law of logarithm for independent and identically distributed arrays is derived more precisely and the sufficient and necessary conditions for the law of logarithm are obtained. 展开更多
关键词 sub-linear expectation capacity exponential inequality extended negative dependence the law of logarithm
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The Convergence of the Sums of Independent Random Variables Under the Sub-linear Expectations 认领 引用 被引量：10
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作者 Li Xin ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2020年第3期224-244,共21页
Let {Xn;n≥1} be a sequence of independent random variables on a probability space(Ω,F,P) and Sn=∑k=1n Xk.It is well-known that the almost sure convergence,the convergence in probability and the convergence in distr... Let {Xn;n≥1} be a sequence of independent random variables on a probability space(Ω,F,P) and Sn=∑k=1n Xk.It is well-known that the almost sure convergence,the convergence in probability and the convergence in distribution of Sn are equivalent.In this paper,we prove similar results for the independent random variables under the sub-linear expectations,and give a group of sufficient and necessary conditions for these convergence.For proving the results,the Levy and Kolmogorov maximal inequalities for independent random variables under the sub-linear expectation are established.As an application of the maximal inequalities,the sufficient and necessary conditions for the central limit theorem of independent and identically distributed random variables are also obtained. 展开更多
关键词 Sub-linear expectation capacity independence Levy maximal inequality central limit theorem
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Donsker’s Invariance Principle Under the Sub-linear Expectation with an Application to Chung’s Law of the Iterated Logarithm 认领 引用 被引量：24
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作者 Li-Xin Zhang 《Communications in Mathematics and Statistics》 2015年第2期187-214,共28页
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 logari... 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. 展开更多
关键词 Sub-linear expectation Capacity Central limit theorem Invariance principle Chung’s law of the iterated logarithm Small deviation
Lindeberg's central limit theorems for martingale-like sequences under sub-linear expectations 认领 引用 被引量：5
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作者 Li-Xin Zhang 《Science China Mathematics》 SCIE CSCD 2021年第6期1263-1290,共28页
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem ... The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established. 展开更多
关键词 capacity central limit theorem functional central limit theorem martingale difference sub-linear expectation
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The Sufficient and Necessary Conditions of the Strong Law of Large Numbers under Sub-linear Expectations 认领 引用 被引量：5
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作者 Li Xin ZHANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第12期2283-2315,共33页
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 ... 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 R∞ under a probability, we give the sufficient and necessary conditions of the strong law of large numbers for independent and identically distributed random variables under the sub-linear expectation, and the sufficient and necessary conditions for the convergence of an infinite series of independent random variables, without the assumption on the continuity of the capacities. A purely probabilistic proof of a weak law of large numbers is also given. 展开更多
关键词 Sub-linear expectation capacity strong convergence law of large numbers
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On the laws of the iterated logarithm under sub-linear expectations 认领 引用 被引量：7
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作者 Li-Xin Zhang 《Probability, Uncertainty and Quantitative Risk》 2021年第4期409-460,共52页
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 distribu... 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.Exponential 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 logarithm.As 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 obtained.In the paper,it is also shown that if the sub-linear expectation space is rich enough,it will have no continuous capacity.The laws of the iterated logarithm are established without the assumption on the continuity of capacities. 展开更多
关键词 Sub-linear expectation Capacity Kolmogorov’s exponential inequality Laws of the iterated logarithm
Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications 认领 引用 被引量：67
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作者 ZHANG LiXin 《Science China Mathematics》 SCIE CSCD 2016年第4期751-768,共18页
Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of indepen... Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng(2008),we introduce the concept of negative dependence of random variables and establish Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations.As an application,we show that Kolmogorov's strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite. 展开更多
关键词 sub-linear expectation capacity Kolmogorov＇s inequality Rosenthal＇s inequality negative dependence strong laws of large numbers
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Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm 认领 引用 被引量：55
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作者 ZHANG LiXin 《Science China Mathematics》 SCIE CSCD 2016年第12期2503-2526,共24页
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. This paper est... 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. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments.For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sublinear expectation for random variables with only finite variances. 展开更多
关键词 sub-linear expectation capacity Kolmogorov＇s exponential inequality negative dependence laws of the iterated logarithm central limit theorem
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Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations 认领 引用
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作者 Feng-xiang FENG Ding-cheng WANG +1 位作者 Qun-ying WU Hai-wu HUANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2024年第3期862-874,共13页
In this article,we study strong limit theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations.We establish general strong law and complete convergence theorems fo... In this article,we study strong limit theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations.We establish general strong law and complete convergence theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations.Our results of strong limit theorems are more general than some related results previously obtained by Thrum(1987),Li et al.(1995)and Wu(2010)in classical probability space. 展开更多
关键词 sub-linear expectation complete convergence complete moment convergence the maximal weighted sums
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