In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated r...In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated random variables. As applications of these inequalities, by employing the notions of residual Cesàro α-integrability and strong residual Cesàro α-integrability, we derive some results on Lp convergence where 1 < p < 2 and complete convergence. In addition, we estimate the rate of convergence in Marcinkiewicz-Zygmund strong law for partial sums of identically distributed random variables.展开更多
The authors achieve a general law of precise asymptotics for a new kind of complete moment convergence of i.i.d. random variables, which includes complete con- vergence as a special case. It can describe the relations...The authors achieve a general law of precise asymptotics for a new kind of complete moment convergence of i.i.d. random variables, which includes complete con- vergence as a special case. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in studies of complete convergence. This extends and generalizes the corresponding results of Liu and Lin in 2006.展开更多
Investigates the convergence of an explicit upwind finite element method, the edge-averaged finite element method to multidimensional scalar conservation laws. Discussion on the finite element scheme and main converge...Investigates the convergence of an explicit upwind finite element method, the edge-averaged finite element method to multidimensional scalar conservation laws. Discussion on the finite element scheme and main convergence theorem; Proofs of the technical lemmas.展开更多
Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of...Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.展开更多
As the EU passes the first AI law,the U.S.grapples with bipartisanship,and China proactively advances the issue-based approach and advocates the Global AI Governance Initiative,will AI become“a force for good,ensurin...As the EU passes the first AI law,the U.S.grapples with bipartisanship,and China proactively advances the issue-based approach and advocates the Global AI Governance Initiative,will AI become“a force for good,ensuring safety,and promoting fairness”?展开更多
Some results in the law of logarithm for NA sequences are obtained, which are similar to the result of id random variables; as a corollary, a sufficient result for the bounbed law of logarithm for NA arrays is given. ...Some results in the law of logarithm for NA sequences are obtained, which are similar to the result of id random variables; as a corollary, a sufficient result for the bounbed law of logarithm for NA arrays is given. Meanwhile, A conjecture for id random variables of Gut is answered in NA setting. Under weaker moment conditions than Su and Qin’s, a stronger convergence resuit than their Theorem 1 is obtained.展开更多
We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in ...We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.展开更多
In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtaine...In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz （1937）, Jamison （1965）, Matula （1992） and Wu （2001） from the independent identically distributed （i.i.d.） case to pairwise NQD sequences.展开更多
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
基金supported by National Natural Science Foundation of China (Grant No.10871217) the SCR of Chongqing Municipal Education Commission (Grant No.KJ090703)
文摘In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated random variables. As applications of these inequalities, by employing the notions of residual Cesàro α-integrability and strong residual Cesàro α-integrability, we derive some results on Lp convergence where 1 < p < 2 and complete convergence. In addition, we estimate the rate of convergence in Marcinkiewicz-Zygmund strong law for partial sums of identically distributed random variables.
基金supported by the National Natural Science Foundation of China(No.10571073)the 985 Program of Jilin University.
文摘The authors achieve a general law of precise asymptotics for a new kind of complete moment convergence of i.i.d. random variables, which includes complete con- vergence as a special case. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in studies of complete convergence. This extends and generalizes the corresponding results of Liu and Lin in 2006.
基金The second author was supported by the China State Major Key project for Basic Researches and theScience .Fund of the Ministry
文摘Investigates the convergence of an explicit upwind finite element method, the edge-averaged finite element method to multidimensional scalar conservation laws. Discussion on the finite element scheme and main convergence theorem; Proofs of the technical lemmas.
基金Supported by the Outstanding Youth Research Project of Anhui Colleges(Grant No.2022AH030156)。
文摘Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.
文摘As the EU passes the first AI law,the U.S.grapples with bipartisanship,and China proactively advances the issue-based approach and advocates the Global AI Governance Initiative,will AI become“a force for good,ensuring safety,and promoting fairness”?
文摘Some results in the law of logarithm for NA sequences are obtained, which are similar to the result of id random variables; as a corollary, a sufficient result for the bounbed law of logarithm for NA arrays is given. Meanwhile, A conjecture for id random variables of Gut is answered in NA setting. Under weaker moment conditions than Su and Qin’s, a stronger convergence resuit than their Theorem 1 is obtained.
基金supported by the National Natural Science Foundation of China(11571052,11731012)the Hunan Provincial Natural Science Foundation of China(2018JJ2417)the Open Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(2018MMAEZD02)。
文摘We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 11061012, the Support Program of the New Century Guangxi China Ten-hundred-thousand Talents Project under Grant No. 2005214, and the Guangxi, China Science Foundation under Grant No. 2010GXNSFA013120.
文摘In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz （1937）, Jamison （1965）, Matula （1992） and Wu （2001） from the independent identically distributed （i.i.d.） case to pairwise NQD sequences.
基金Supported by grants from the NSF of China(Grant Nos.11731012,12031005)Ten Thousands Talents Plan of Zhejiang Province(Grant No.2018R52042)+1 种基金NSF of Zhejiang Province(Grant No.LZ21A010002)the Fundamental Research Funds for the Central Universities。
文摘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.
