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| 1 | Precise Rates in the Law of the Logarithm for the Moment Convergence in Hilbert Spaces显示文摘让 { X, X n ;n ≥
1 } i.i.d 随机变量的一个序列在一个真实可分离的 Hilbert 空格正在拿值(H, ‖
· ‖
) 与协变性操作员 Σ
。集合 S n = X 1+ X 2+...+ X n , n ≥
1。我们证明为 b >
−1 ,如果,那成立前= 0 ,并且E‖X‖ 2(log ‖X‖)3b∨(b+4)<
∞
,在 Y 是拿的一个 Gaussian 随机的变量的地方,与平均数零在一个真实可分离的 Hilbert 空格珍视并且协变性操作符Σ
,并且σ
2表示Σ
的最大的特征值。 | Ke Ang FU Li Xin ZHANG | 2009 | Acta Mathematica Sinica,English Series2009，25，2： | 2 |
| 2 | A Nonclassical LIL for Geometrically Weighted Series in Banach Space显示文摘Let {X, Xn ; n ≥ 0} be a sequence of independent and identically distributed random variables, taking values in a separable Banach space (B,||·||) with topological dual B* . Considering the geometrically weighted series ξ(β) =∑∞n=0βnXn for 0 < β < 1, and a sequence of positive constants {h(n), n ≥ 1}, which is monotonically approaching infinity and not asymptotically equivalent to log log n, a limit result for(1-β2)1/2||ξ(β)||/(2h(1/(1-β2)))1/2 is achieved. | Ke Ang FU Xiao Rong YANG Wei HUANG | 2013 | Acta Mathematica Sinica,English Series2013，29，7： | 1 |
| 3 | A Self-normalized Law of the Iterated Logarithm for the Geometrically Weighted Random Series显示文摘Let {X, X_n; n ≥ 0} be a sequence of independent and identically distributed random variables with EX=0, and assume that EX^2I(|X| ≤ x) is slowly varying as x →∞, i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series Σ~∞_(n=0)β~nX_n(0 < β < 1) is obtained, under some minimal conditions. | Ke Ang FU Wei HUANG | 2016 | Acta Mathematica Sinica,English Series2016，32，3： | 0 |
| 4 | Convergence Rates of Tail Probabilities for Sums under Dependence Assumptions显示文摘让 { X, X 1, X 2, ...} 是零个平均数严格地静止 ? 混合顺序。集合 S n = 危 k=1 n X k 和 f (x p )= 危 n=1 鈭 ? n r ? 2P (| S n |鈮 ? x p ) 。什么时候?>() 1/p,为 p > 1/2 和 r > 1,为鈭的条件??鈭 ? f (x p dx < 保持的鈭 ? 被建立由和强壮的近似使用联合方法,它与传统的使相称和 Hoffman-J 不同 ? rgensen 不平等。关键词完全的集中 - 混合序列 - 强壮的近似先生(2000 ) 题目分类 60F15 由中国的国家自然科学基础支持了(资助 Nos. 10771192 并且 10671176 ) | Xiao Rong YANG Wei Dong LIU Ke Ang FU Lin Xin ZHANG | 2010 | Acta Mathematica Sinica,English Series2010，26，8： | 0 |
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