加权AANA随机变量和的一致强收敛速度

为了完善 AANA 序列的极限理论,利用三级数定理、Borel-Cantelli 引理及一些概率不等式,研究了AANA 随机变量序列的函数加权和。在一定的条件下,得到了其一致强收敛速度为n？13 log n,推广了关于NA随机变量序列的相应结果。     

α-混合随机序列最近邻密度估计的强相合收敛速度

设{Xi）i=1^∞是一维平稳序列，具有公共的未知密度f（x），在{Xi}i=1^∞是α-混合的条件下，给出了f（x）基于前礼个观测值{Xi}i=1^∞的最近邻密度估计的强相合收敛速度，当f（x）满足适当条件，收敛速度可达到0（n^-1/3（ln n）^4（1＋p）／3））．     

NA序列部分和的完全收敛性

本文讨论了非平稳NA随机变量序列部分和的完全收敛性,获得了一般形式的完全收敛速度与矩条件之间的等价关系,其结果与独立情形一致,从而证实了NA序列与独立序列有着极为类似的完全收敛性．     

由非同分布NA序列产生的移动平均过程的完全收敛性

设{Y_n,-∞相似文献   

NA序列部分和的矩完全收敛性

讨论了NA序列部分和的矩完全收敛性,在一定条件下获得了NA序列矩完全收敛的充要条件,显示了矩完全收敛和矩条件之间的关系,将独立同分布随机变量序列矩完全收敛的结果推广到NA序列,得到了与独立随机变量序列情形类似的结果.     

不同分布NA序列加权和的完全收敛性

本文讨论了不同分布NA随机变量序列加权和的完全收敛性，获得了较[7]中的定理1及定理A更为一般的安全收敛性，并得到了完全收敛速度与矩条件之间的等价关系。     

依概率收敛与依分布收敛的关系

本探讨了随机变量序列依概率收敛与依分布收敛的关系,并给出了一个依分布收敛能保证依概率收敛的最弱的条件,即：设分布函数列{Fn（x）}弱收敛于连续的分布函数F(x),则存在随机变量序列{ξn}和随机变量ξ,它们分别以{Fn（x）}和F（x）为其对应的分布函数和分面函数,且{ξn}依概率收敛于ξ。     

NA序列的重对数矩收敛的精确渐近性

假设{X_n,n≥1}为一列严平稳的NA随机变量,期望为零,方差有限.设S_n=∑_(i=1)~n∑X_i,M_n=max_(1≤i≤n)|S_i|.在适当的条件下,得到了一类NA序列部分和部分和最大值重对数矩收敛的精确渐近性.     

不同分布的NA列的加权和的强收敛速度

本文得到了不同分布的NA列的加权和的完全收敛性，在权序列{ank，1≤k≤n，n∈N}满足不同条件的情况下，讨论了使得加权和完全收敛的关于X的矩的阶数，尤其是在一定的条件下，得到了只要求X很低的阶数的矩。得到了令人满意的结果．     

可交换随机变量序列重对数律的收敛速度

本文讨论了可交换随机变量序列{Xn:n≥1)重对数律的收敛速度,得到了可交换随机变量序列与独立序列类似的极限性质,同时给出了可交换序列重对数律收敛速度的一种描述.     

Über Konvergenz von Spektralfolgen der stabilen Homotopietheorie

We discuss the problem of convergence of spectral sequences that arise from a filtration of a spectrum in Boardman's stable homotopy category by applying a generalized homology, homotopy or cohomology theory. The criteria we get give e.g. the convergence of the Adams spectral sequence for a generalized homology theory in certain cases (using similar methods this equestion has been considered independently by J. F. Adams in his forthcoming Chicago lecture notes), and some results on the Adams cohomology spectral sequence including the well-known convergence properties in case of singular cohomology with Z_p-coefficients and complex cobordism.     

关于正整数的立方部分

对于任意正整数n，定义u(n)为不大于n的最大立方数，v(n)为不小于n的最小立方数．研究了数列{u(n))和{v(n)}的性质，并给出了两个有趣的渐近公式．     

依概率收敛与依分布收敛的关系

本文探讨了随机变量序列依概率收敛与依分布收敛的关系 ,并给出了一个依分布收敛能保证依概率收敛的最弱的条件 ,即 :设分布函数列 { Fn(x) }弱收敛于连续的分布函数 F(x) ,则存在随机变量序列{ξn}和随机变量ξ,它们分别以 { Fn(x) }和 F(x)为其对应的分布函数列和分布函数 ,且 {ξn}依概率收敛于ξ.     

一种预测—校正式单点迭代方法

本文以Ｎｅｗｔｏｎ迭代法（ｘｎ＋１＝ｘｎ－ｆ（ｘｎ）／ｆ′（ｘｎ），收敛阶为２）为基础，给出了一种新的实用的预测—校正式单点迭代方法（ｘｎ＋１＝ｘｎ－ｕ（ｘｎ）ｆ（ｘｎ）＋１２ｆ（ｘｎ－ｕ（ｘｎ））ｆ（ｘｎ）－１２ｆ（ｘｎ－ｕ（ｘｎ））收敛阶为４）．该方法不仅公式简洁，计算方便，计算量小，而且收敛阶高，收敛速度快     

A New Uniform Convergence for Partial Functions

Suppose X, Y are topological spaces. In this paper maps are not necessarily continuous. A map f from a non-empty subset of X to Y is called a partial map. Partial maps occur as inverse functions in elementary analysis, as solution of ordinary differential equations, as utility functions in mathematical economics, etc. In many applications, X and Y are metric spaces and there is a need to have a uniform convergence on a family of partial functions. Since partial maps do not have a common domain, the usual uniform convergence (u.c.) is not available. Noting that in many situations, all maps of a family under consideration, have a common range, we define a new uniform convergence (n.u.c.) that is complementary to the usual one. This n.u.c. does not preserve continuity but preserves (uniform) openness. Its usefulness stems from the fact that it can be used when u.c. cannot be defined. Moreover, in some situations where both u.c. and n.u.c. are available, the latter satisfies our intuition but not the former. We give applications to ODE's and throw some light on earlier literature.     

Non-Nehari manifold method for periodic discrete superlinear Schrödinger equation

We consider the nonlinear difference equations of the form Lu=f(n, u), n∈Z, where L is a Jacobi operator given by(Lu)(n)=a(n)u(n+1)+a(n-1)u(n-1)+b(n)u(n) for n∈Z, {a(n)} and {b(n)} are real valued N-periodic sequences, and f(n, t) is superlinear on t. Inspired by previous work of Pankov [Discrete Contin. Dyn. Syst., 19, 419-430(2007)] and Szulkin and Weth [J. Funct. Anal., 257, 3802-3822(2009)], we develop a non-Nehari manifold method to find ground state solutions of Nehari-Pankov type under weaker conditions on f. Unlike the Nehari manifold method, the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the Nehari-Pankov manifold by using the diagonal method.     

An almost sure invariance principle for stationary ergodic sequences of Banach space valued random variables

Summary In this paper we establish an almost sure invariance principle with an error termo((t log logt)^1/2) (ast) for partial sums of stationary ergodic martingale difference sequences taking values in a real separable Banach space. As partial sums of weakly dependent random variables can often be well approximated by martingales, this result also leads to almost sure invariance principles for a wide class of stationary ergodic sequences such as ø-mixing and -mixing sequences and functionals of such sequences. Compared with previous related work for vector valued random variables (starting with an article by Kuelbs and Philipp [27]), the present approach leads to a unification of the theory (at least for stationary sequences), moment conditions required by earlier authors are relaxed (only second order weak moments are needed), and our proofs are easier in that we do not employ estimates of the rate of convergence in the central limit theorem but merely the central limit theorem itself.     

Convergence Rates of Wavelet Estimators in Semiparametric Regression Models Under NA Samples

Consider the following heteroscedastic semiparametric regression model:yi =XTiβ + g(ti) + σiei, 1 ＜ i ≤ n,where {Xi,1 ＜ i ＜ n} are random design points,errors {ei,1 ＜ i ＜ n} are negatively associated (...     

A law of the iterated logarithm for kernel estimators of regression functions

Summary For fixed design regression data kernel estimation is widely used to estimate _(v)(t), thev-th derivative of (t). Denoting such an estimator by this paper is concerned with the almost sure convergence of . It is shown that under several inserting procedures a law of iterated logarithm holds.     

A Tauberian Theorem for Ergodic Averages,Spectral Decomposability,and the Dominated Ergodic Estimate for Positive Invertible Operators

Suppose that (,) is a -finite measure space, and 1 < p < . Let T:L^p( L ^p() be a bounded invertible linear operator such that T and T ^–1 are positive. Denote by _n(T) the nth two-sided ergodic average of T, taken in the form of the nth (C,1) mean of the sequence {T^j+T^–j}_{j =1} . Martín-Reyes and de la Torre have shown that the existence of a maximal ergodic estimate for T is characterized by either of the following two conditions: (a) the strong convergence of E_n(T)_n=1 ; (b) a uniform A _p p estimate in terms of discrete weights generated by the pointwise action on of certain measurable functions canonically associated with T. We show that strong convergence of the (C,2) means of {T^j+T^–j}_j=1 already implies (b). For this purpose the (C,2) means are used to set up an `averaged' variant of the requisite uniform A _p weight estimates in (b). This result, which can be viewed as a Tauberian-Type replacement of (C,1) means by (C,2) means in (a), leads to a spectral-theoretic characterization of the maximal ergodic estimate by application of a recent result of the authors establishing the strong convergence of the (C,2)-weighted ergodic means for all trigonometrically well-bounded operators. This application also serves to equate uniform boundedness of the rotated Hilbert averages of T with the uniform boundedness of the ergodic averages E_n(T)_{n = 1} .