On Complete Convergence for Nonstationary ϕ-Mixing Random Variables

In this article, we study the complete convergence for non-stationary ?-mixing random variables, especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for ?-mixing random variables. Our result generalizes the corresponding one of Shao (1988 Shao, Q.M. (1988). A moment inequality and its applications. Acta Mathematica Sinica 31(6):736–747. [Google Scholar]) and improves the corresponding one of Peligrad (1985a Peligrad, M. (1985a). Convergence rates of the strong law for stationary mixing sequences. Z. Wahrsch. verw. Gebiete. 70:307–314.[Crossref], [Web of Science ®] , [Google Scholar]) and Wang (1987 Wang, D.C. (1987). The complete convergence of the sums for the stationary sequence of ?-mixing random variables. J. Syst. Sci. Mathemat. Sci. 7(4):352–359. [Google Scholar]).     

Estimation of regression vectors in linear mixed models with Dirichlet process random effects

The Dirichlet process has been used extensively in Bayesian non parametric modeling, and has proven to be very useful. In particular, mixed models with Dirichlet process random effects have been used in modeling many types of data and can often outperform their normal random effect counterparts. Here we examine the linear mixed model with Dirichlet process random effects from a classical view, and derive the best linear unbiased estimator (BLUE) of the fixed effects. We are also able to calculate the resulting covariance matrix and find that the covariance is directly related to the precision parameter of the Dirichlet process, giving a new interpretation of this parameter. We also characterize the relationship between the BLUE and the ordinary least-squares (OLS) estimator and show how confidence intervals can be approximated.     

A self-normalized central limit theorem for a ρ-mixing stationary sequence

We investigate a self-normalized central limit theorem for a ρ-mixing stationary sequence {X_i, i ? 1} of random variables such that L(x) ? E(X²₁I{|X₁| ? x}) is a slowly varying function as x → ∞. The results obtained generalize the results of Gine, Gotze, and Mason (1997) and Mason (2005 Mason, D. M. 2005. The asymptotic distribution of self-normalized triangular arrays. Journal of Theoretical Probability 18 (4):853–70.[Crossref], [Web of Science ®] , [Google Scholar]) to ρ-mixing sequences.     

一般散度型线性抛物方程Wp（1,0）弱解的存在性

利用Stampacchia内插定理,研究了一类带有混合边界条件的散度型线性抛物方程Wp1,0弱解的存在性.     

一类非线性混林发展系统的模型

讨论了一类非线性混林发展系统模型,利用特征理论、不动点定理和迭代技术,证明了这个问题古典解存在的唯一性。     

以{2~n-1,2~n,2~n+1}为基的余数系统2~n高性能缩放

数值缩放(scaling)的高效VLSI实现是基于余数系统(RNS)的DSP系统的关键问题之一。该文提出了有符号余数系统数值缩放通用算法,并结合基为{2n-1,2n,2n+1}的余数系统特性提出了其优化的2n缩放算法和VLSI实现结构,明确给出了在进行有符号RNS整数缩放时负数情况下所引入的修正常量计算方法。分析表明该方法较级联n个1bit缩放模块实现余数系统2n缩放具有更好的速度、面积和功耗特性,从而易于实现基于RNS的DSP系统。