非平稳NA序列部分和的精确渐近性

本文探讨了非平稳NA序列部分和的精确渐近性．以前的文献在讨论NA序列此类极限性质时都附加有强平稳条件的限制,这必然会给一些问题的研究带来不便．周知,非平稳NA序列在许多实际问题中是大量存在的,所以解除强平稳条件的束缚具有较大的理论和实际意义,这正是本文的目的之所在,同时本文也将已有的一些结果包含成为特殊情形．     

��ƽ��ND���в��ֺ͵ľ�ȷ������

In this paper, by using central limit theorem of ND sequences and probability inequality, the precise asymptotics for partial sums of nonstationary ND sequences is investigated, and the same results with it under that of NA sequences are obtained.     

独立与NA列部分和的精致渐近性

令{X,Xi:i≥1)为属于非退化稳定分布一般吸引场的独立同分布随机变量列,Sn=∑i=1nXi.本文对十分广泛的拟权函数和边界函数得到了Sn的精致渐近的结果和正态吸引场强平稳NA列部分和的精致渐近的结果,改进并推广了Wang等的结果,从而使此前关于独立列和NA列部分和精致渐近性方面的许多经典的和最新的结果都可以包括在本文的框架之内.     

�����򲿷ֺ͵���ȫ�صľ�ȷ������

设{X,Xn;n≥1}为吸引域为正态吸引域的独立同分布的随机变量序列,本文证明了其自正则部分和的完全矩的精确渐近性.     

A General Law of Precise Asymptotics for the Complete Moment Convergence

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 convergence 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.     

Asymptotics of Sums of Cosine Series with Fractional Monotonicity Coefficients

Mathematical Notes - The paper examines the following question: Under what orders of monotonicity are the upper and lower bounds of the sum of a cosine series near zero valid if they are obtained...     

Strassen-Type Law of the Iterated Logarithm for Self-normalized Sums

Let {X,X _n ,n≥1} be a sequence of independent identically distributed random variables with EX=0 and assume that EX ² I(|X|≤x) is slowly varying as x→∞. In this paper it is shown that a Strassen-type law of the iterated logarithm holds for self-normalized sums of such random variables, i.e., when X is in the domain of attraction of the normal law.     

自正则化和Davis大数律和重对数律的精确渐近性

本文证明了自正则化Davis大数律和重对数律的精确渐近性, 即 {\heiti\bf 定理1}\hy 设$\ep X=0$, 且$\ep X^2I_{(|X|\leq x)}$在无穷远处是缓变函数, 则$\lim_{\varepsilon\searrow0}\varepsilon^2\tsm_{n\geq3}\frac{1}{n\log n}\pr\Big(\Big|\frac{S_n}{V_n}\Big|\geq\varepsilon\sqrt{\log\log n}\Big)=1.${\heiti\bf 定理2}\hy 设$\ep X=0$, 且$\ep X^2I_{(|X|\leq x)}$在无穷远处是缓变函数, 则对本文证明了目正则化Davis大数律和重对数律的精确渐近性,即定理1设EX=0,且EX~2I_(|x|≤x)在无穷远处是缓变函数,则■定理2设EX=0,且EX~2I_(|x|≤x)在无穷远处是缓变函数,则对0≤δ≤1,有■其中N为标准正态随机变量．     

Asymptotics and Formulas for Cubic Exponential Sums

Several asymptotic expansions and formulas for cubic exponential sums are derived. The expansions are most useful when the cubic coefficient is in a restricted range. This generalizes previous results in the quadratic case and helps to clarify how to numerically approximate cubic exponential sums and how to obtain upper bounds for them in some cases.     

NA序列完全矩收敛精确渐近性的一般结果

本文利用NA序列的弱收敛定理及概率不等式,证明了其完全矩收敛精确渐近性的一般结果,改进并推广了已有的结果.     

Uniform Convergence of Hyperbolic Partial Sums of Multiple Fourier Series

It follows from results of A. Yudin, V. Yudin, E. Belinskii, and I. Liflyand that if $m \geqslant 2$ and a $2\pi $ -periodic (in each variable) function $f(x) \in C(T^m )$ belongs to the Nikol'skii class $h_\infty ^{(m - 1)/2} (T^m )$ , then its multiple Fourier series is uniformly convergent over hyperbolic crosses. In this paper, we establish the finality of this result. More precisely, there exists a function in the class $h_\infty ^{(m - 1)/2} (T^m )$ whose Fourier series is divergent over hyperbolic crosses at some point.     

Convergence of Partial Sums of Dirichlet Series and Rational Approximation of Functions

A rational approximation on [0,1) of functions that are analytic in the unit disk is investigated.     

随机向量自正则和的重对数律

本文给出了独立随机向量序列自正则和的重对数律成立的一个充分条件.     

U-统计量的精致渐近性

设{X_n．n≥1}是一非退化的i．i．d．随机变量序列,U_n是以二维Borel可测对称函数h(x,y)为核函数的U-统计量．记U_n=2/(n(n-1))Σ_≤i≤j≤nh(X_i,X_j)．本文分别在核函数h(x,y)只有4/3阶矩或4/3+δ,0＜δ≤1的情况下,对非常广泛的一类权函数(x)与边界函数b(x)得到了如下关于U-统计量U_n的精致渐近性:不仅使得已有的结果成为我们的特况,还大大降低了其中的矩条件．     

Gauss和与广义Kloosterman和的几个新的恒等式

主要应用Gauss和的性质和解析方法来研究Gauss和与广义Kloosterman和之间的关系,并且给出了几个有趣的恒等式.     

New Exceptional Sets and Convergence of the Square Partial Sums of Walsh–Fourier Series

For double Walsh–Fourier series and with f ∈ L~2([0, 1) × [0, 1)) we prove two almost orthogonality results relative to the linearized maximal square partial sums operator S_(N(x,y))f(x, y).Assumptions are N(x, y) non-decreasing as a function of x and of y and, roughly speaking, partial derivatives with approximately constant ratio ■≌2~(n_0) for all x and y, where n_0 is any fixed non-negative integer. Estimates, independent of N(x, y) and n_0, are then extended to L~r, 1 r 2.We give an application to the family N(x, y) = λxy on [0, 1) × [0, 1), any λ 10.     

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.     

带不同分布增量的随机和的局部渐近性

在Asmussen,Foss and Korshunov(J.Theoretical Probab.,2003,16(2):489-518)的基础上,讨论了支撑在(-∞,∞)上的不同分布的卷积的封闭性及带上述不同分布增量的局部渐近性.上述分布包括了常见的轻尾分布和重尾分布.     

带不同分布增量的随机和的局部渐近性

在Asmussen,Foss and Korshunov(J.Theoretical Probab.,2003,16(2)489-518)的基础上,讨论了支撑在(-∞,∞)上的不同分布的卷积的封闭性及带上述不同分布增量的局部渐近性.上述分布包括了常见的轻尾分布和重尾分布.