We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale differen...We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.展开更多
Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are...Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.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
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
Under very general weight function, we discuss the convergence of Jamison-type weighted sums of pairwise negatively quadrant dependent (NQD) r.v.'s. The results on i.i.d. setting of [3] and [1] are extended and ge...Under very general weight function, we discuss the convergence of Jamison-type weighted sums of pairwise negatively quadrant dependent (NQD) r.v.'s. The results on i.i.d. setting of [3] and [1] are extended and generalized. As corollaries, we obtain some results of [11].展开更多
基金Supported by the National Natural Science Foundationof China (10671149)
文摘We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.
文摘Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.
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].
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.
基金Supported by the National Natural Science Foundation of China (No.10171079 NO.10071081)the Science Foundation of Tong ji University.
文摘Under very general weight function, we discuss the convergence of Jamison-type weighted sums of pairwise negatively quadrant dependent (NQD) r.v.'s. The results on i.i.d. setting of [3] and [1] are extended and generalized. As corollaries, we obtain some results of [11].
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
