In this paper, Kolmogorov-type inequality for negatively superadditive dependent （NSD） random variables is established. By using this inequality, we obtain the almost sure convergence for NSD sequences, which extend...In this paper, Kolmogorov-type inequality for negatively superadditive dependent （NSD） random variables is established. By using this inequality, we obtain the almost sure convergence for NSD sequences, which extends the corresponding results for independent sequences and negatively associated （NA） sequences. In addition, the strong stability for weighted sums of NSD random variables is studied.展开更多
In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong...In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.展开更多
In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the c...In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].展开更多
Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stocha...Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.展开更多
We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to c...We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.展开更多
本文研究了条件为C_V(|X|~p)<∞, even ê(|X|p)≤C_V(|X|p), 0 <p≤2的次线性期望空间下广义ND序列的加权和的几乎处处收敛.作为应用,我们的结果扩展了SILVA(2015)在概率空间下的相应结果.此外,本文的结果扩展了次线性期望...本文研究了条件为C_V(|X|~p)<∞, even ê(|X|p)≤C_V(|X|p), 0 <p≤2的次线性期望空间下广义ND序列的加权和的几乎处处收敛.作为应用,我们的结果扩展了SILVA(2015)在概率空间下的相应结果.此外,本文的结果扩展了次线性期望空间下加权和的几乎处处收敛.展开更多
In this article the supercritical bisexual Galton-Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for th...In this article the supercritical bisexual Galton-Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for the L^1 convergence are given for the process with the suitably normed condition.展开更多
For a double array of blockwise M-dependent random variables {Xmn,m ≥ 1,n ≥ 1}, ∑i^m=1 ∑^nj=1 strong laws of large numbers are established for double sums ∑m i=1 ∑j^n=1 ij, m≥ 1, n 〉 1. The main results are ob...For a double array of blockwise M-dependent random variables {Xmn,m ≥ 1,n ≥ 1}, ∑i^m=1 ∑^nj=1 strong laws of large numbers are established for double sums ∑m i=1 ∑j^n=1 ij, m≥ 1, n 〉 1. The main results are obtained for （i） random variables {Xmn, m≥ 1, n ≥ 1} being non-identically distributed but satisfy a condition on the summability condition for the moments and （ii） random variables {Xmn, m ≥ 1, n ≥ 1} being stochastically dominated. The result in Case （i） generalizes the main result of M6ricz et al. [J. Theoret. Probab., 21, 660-671 （2008）] from dyadic to arbitrary blocks, whereas the result in Case （ii） extends a result of Gut [Ann. Probab., 6, 469-482 （1978）] to the bockwise M-dependent setting. The sharpness of the results is illustrated by some examples.展开更多
In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed...In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed the implication of the conditions in previous papers.Then we apply these consequences to B-valued random variables,and greatly improve the original results of the strong convergence of the general Jamison weighted sum.Furthermore,our discussions are useful to the corresponding questions of real-valued random variables.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11171001,11201001 and 11126176)Natural Science Foundation of Anhui Province(1208085QA03)Academic Innovation Team of Anhui University(Grant No.KJTD001B)
文摘In this paper, Kolmogorov-type inequality for negatively superadditive dependent （NSD） random variables is established. By using this inequality, we obtain the almost sure convergence for NSD sequences, which extends the corresponding results for independent sequences and negatively associated （NA） sequences. In addition, the strong stability for weighted sums of NSD random variables is studied.
基金the National Natural Science Foundation of China(10671149)
文摘In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.
基金supported by the National Natural Science Foundation of China(1106101270871104)the Program to Sponsor Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning and the Plan of Jiangsu Specially-appointed Professors
文摘In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].
文摘Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.
基金Supported by the National Natural Science Foundation of China (10671149)
文摘We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.
基金Supported by the National Natural Science Foundation of China(11661029)the Support Program of the Guangxi China Science Foundation(2015GXNSFAA139008,2018GXN SFAA281011)
文摘本文研究了条件为C_V(|X|~p)<∞, even ê(|X|p)≤C_V(|X|p), 0 <p≤2的次线性期望空间下广义ND序列的加权和的几乎处处收敛.作为应用,我们的结果扩展了SILVA(2015)在概率空间下的相应结果.此外,本文的结果扩展了次线性期望空间下加权和的几乎处处收敛.
文摘In this article the supercritical bisexual Galton-Watson branching processes with the immigration of mating units is considered. A necessary condition for the almost sure convergence, and a sufficient condition for the L^1 convergence are given for the process with the suitably normed condition.
文摘For a double array of blockwise M-dependent random variables {Xmn,m ≥ 1,n ≥ 1}, ∑i^m=1 ∑^nj=1 strong laws of large numbers are established for double sums ∑m i=1 ∑j^n=1 ij, m≥ 1, n 〉 1. The main results are obtained for （i） random variables {Xmn, m≥ 1, n ≥ 1} being non-identically distributed but satisfy a condition on the summability condition for the moments and （ii） random variables {Xmn, m ≥ 1, n ≥ 1} being stochastically dominated. The result in Case （i） generalizes the main result of M6ricz et al. [J. Theoret. Probab., 21, 660-671 （2008）] from dyadic to arbitrary blocks, whereas the result in Case （ii） extends a result of Gut [Ann. Probab., 6, 469-482 （1978）] to the bockwise M-dependent setting. The sharpness of the results is illustrated by some examples.
基金Research supported by National Science Foundation of China(No.10071081)special financial support of Chinese Academy of Sciences
文摘In this paper,two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods,their properties and relationships are system- atically discussed.We also analysed the implication of the conditions in previous papers.Then we apply these consequences to B-valued random variables,and greatly improve the original results of the strong convergence of the general Jamison weighted sum.Furthermore,our discussions are useful to the corresponding questions of real-valued random variables.
