THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))

Let G = SU（2, 2）, K = S（U（2） × U（2））, and for l ∈ Z, let {Tl}l∈z be a one-dimensional K-type and let El be the line bundle over G/K associated to Tl. It is shown that the Tl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.

Functional Shige Peng’s Central Limit Theorems for Martingale Vectors

In this paper,the functional central limit theorem is established for martingale like ran-dom vectors under the framework sub-linear expectations introduced by Shige Peng.As applications,the Lindeberg central limit theorem for independent random vectors is established,the sufficient and necessary conditions of the central limit theorem for independent and identically distributed random vectors are found,and a Lévy’s characterization of a multi-dimensional G-Brownian motion is obtained.

A Note on the Almost Sure Central Limit Theorem in the Joint Version for the Maxima and Partial Sums of Certain Stationary Gaussian Sequences

Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves that on the almost sure central limit theory previously obtained by Marcin Dudzinski [1]. Our result reaches the optimal form.

The Central Limit Theorem on SU(n,1)/S(U(n)×U(1))

Let G = SU（n, 1）, K = S（U（n） × U（1））, and for l ∈Z, let {T;},l∈Z be a one- Dimensional K-type and let Et be the line bundle over G/K associated to Tl. In this work we obtain a central limit theorem for the space Et.

A RANDOM FUNCTIONAL CENTRAL LIMIT THEOREM FOR PROCESSES OF PRODUCT SUMS OF LINEAR PROCESSES GENERATED BY MARTINGALE DIFFERENCES

A random functional central limit theorem is obtained for processes of partial sums andproduct sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding results on processes of partial sums of linear processesgenerated by strictly stationary martingale differences, which can be found in [5].

Almost sure central limit theorems for random functions

Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|Rn| <∞and Rn = o(n^(1/2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.

Characteristic Functions over C*-Probability Spaces

Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.

Lindeberg's central limit theorems for martingale-like sequences under sub-linear expectations

The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.

Central limit theorem for the occupation time of catalyticsuper-Brownian motion

The catalytic super_Brownian motion has been considered. If both the catalytic medium process Q and CSBM started with Lebesgue measure λ, the central limit theorem for occupation time of CSBM has been obtained in dimension 3 for P-λ_a.s.Q.

基于多尺度EMD的激光雷达信号分段去噪

介绍了一种新的信号去噪方法。针对激光雷达信号和 EMD 信号分解的特点,结合统计检测理论,利用中心极限定理和 Grubbs 判据对信号强度起伏的随机性进行检测。检测出的信号强突变部分视为信号的发展趋势保留不参与 EMD 分解,其余部分则使用 EMD 方法分解。对分段处理的信号用半软阈值限幅的办法重构;重构信号可能出现的 pseudo-Gibbs 现象,采用平移不变量去噪原理处理。实测信号的处理结果表明了这种去噪方法的有效性,即能取得较好的去噪效果,又能较好的保留信号的突变信息和强突变信息.

部分和乘积的几乎处处中心极限定理

设{X_n,n≥1}是独立同分布正的随机变量序列,E(X_1)=μ>0,Var(X_1)=σ~2,变异系数γ=σ/μ.g是满足一定条件的无界可测函数,证明了其中F(·)是随机变量e^(2^(1/2)ξ)的分布函数,ξ是服从标准正态分布的随机变量.

随机元序列几乎处处中心极限定理的推广

讨论随机元序列和随机变量序列函数的几乎处处中心极限定理,推广了经典几乎处处中心极限定理中的权重,并改进了经典几乎处处中心极限定理的证明.

随机变量序列函数的几乎处处中心极限定理

该文证明了随机元序列的一个一般的几乎处处中心极限定理,并把这一结论应用于随机变量序列的函数.

关于Lupas-Baskakov算子的点态逼近估计

综合利用概率论-中心极限定理的一种渐近展开形式和Bojanic- Cheng方法结合分析技巧研究了Lupas -Baskakov算子对局部有界函数的点态逼近估计,进一步证明了此估计在连续点处是渐近最优的,并给出了Lupas -Baskakov算子关于单调函数和凸函数的几何性质.

由渐近线性坐标负相依产生的平稳线性过程的泛函中心极限定理

对平稳线性过程Xt=∑∞j=0ajεt-j进行讨论,其中{εt;t∈Z+}为平稳的渐近线性坐标负相依(ALNQD)随机变量序列,满足Eεt=0,Eε2t<∞,以及对某个δ>0有supt∈Z+E|εt|2+δ<∞成立,且常数aj满足∑∞j=0|aj|<∞,得到了一个泛函中心极限定理.

无线智能电表信道路径损耗建模

为适应下一代微功率无线抄表技术发展的需要,针对470~510 MHz特定频段在室内和室外环境中进行信道特性测量并提取信道特性参数,建立路径损耗模型。测量过程中,发射端使用SMW200A矢量信号发生器发送信号,利用频域测量系统的扫频测量法,在室内办公室环境和室外郊区环境中抓取测量数据,同时考虑信号在室内传输过程中墙壁、门窗开闭以及室外行人、车辆、树木等障碍物的影响,分析其大尺度衰落特性。根据测量数据,利用最小二乘法和中心极限定理估算路径损耗模型中的路径损耗因子 n 和标准偏差σ,得出在室内视距情况下470~510 MHz频段的路径损耗模型和室外郊区空旷地带的路径损耗模型。测量和仿真结果表明,该路径损耗模型能较好地预测接收信号强度,为后续测量和抄表业务部署提供依据。

Szasz型算子的函数类逼近

著名的Szasz-Durrmeyer算子的逼近性质已有很多成果,但关于函数类的逼近研究还不多,应用概率论的中心极限定理给出Szasz-Durrmeyer算子的函数类逼近的上下界估计.

关于Post-Gamma算子的点态近估计

综合利用概率论中的中心极限定理的一种渐近展开形式和Bojanic-Cheng方法,研究了Post-Gamma算子 对局部有界函数的点态逼近估计,得到精确的逼近阶,并进一步证明了此估计在连续点处是渐进最优的.

Lupas-Bezier型算子列对局部有界函数的点态逼近估计

利用中心极限定理的Berry-Esseen界估计和Bojanic-Cheng’s方法,并结合分析技巧得到了Lupas-Bezier型算子列对局部有界函数的点态逼近估计,所得结果推广了已有的结果.