关于m型序列的密集区域

本文估计序列{|cm|^1/m}的密集区域，其中{cm}是m型的。     

一类随机变量序列部分和的大偏差

设{xn，n≥1}是鞅差序列，Sn=∑i=1^n Xi，Xi∈L^p，i≥1，文章研究了混合序列和M-Z序列部分和Sn的大偏差，并得到了和鞅差序列类似的结果．     

齐次Moran集的Bouligand维数

设m({nk}k≥1,{Ck}k≥1是由{nk}k≥1,{Ck}k≥1所确定的齐次Moran集类，其中{nk}k≥1是正整数序列，{Ck}k≥1是正实数列。本文确定了m中元素的上（下）Bouligand维数的最大、小值之间的数s，存在m中的元素使其上（下）Bouligand维数值为s。还讨论了齐次Cantor集与偏齐次Cantor集的Bouligand维数存在性之间的关系。     

一类双重时间序列模型的预报

满足 x_t-A_0=(θ_t+α)x_t-1+α_t的时间序列模型称为双重时序模型.其中{α_t}是正态平稳白噪声序列,{θ_t}为一个随机序列.本文给出了当{θt}服从 AR(1)或 MA(1)模型时,{x_t}的多步最小方差预报及其与适时线性最小方差预报的计算机模拟对比。     

关于任意随机变量序列配重和的一类强偏差定理

设{Xn,n≥1}是在E={0，1)中取值的二值随机序列，{an，n≥1}是[0，1]中取值的一列常数，Wn(ω)=n∑i=1aiXi(ω)，本文利用区间剖分法[1],[2]构造单调函数，研究任意二值随机序列配重和Wn(ω)的一类用不等式表示的定理，即强偏差定理．     

关于任意随机变量序列泛函的强极限定理

本文在k是固定的正整数，{fn}是R^k 1上的Borel可测函数列时，得到了任意随机变量序列{Xrn≥0}的泛函{fn(Xn-k,…,Xn)}的强极限定理，它是Chung的关于独立随机变量序列的强大数律的推广，作为推论，得到了k重非齐次马尔科夫链的一类强极限定理．     

关于k阶记录时间与k阶记录值的联合分布

设独立同分布随机变量序列{x_nj n≥1}的分布函数F(x)=p(x₁(k)(n);n≥1},{X^(k)(n);n≥1} 分别为{x_nj n≥1}的K阶记录时间序列和k阶记录值序列.本文我们用直接方法求出了{U^(k)(i),X^(k)(i);1≤i≤n}的联合分布，从而证明了k阶记录时间序列及k阶记录值序列的马氏性，并导出了它们之间的一     

和的乘积的重对数律

设{X,X_n,n≥1}是独立的或φ -混合的或 ρ -混合的正的平稳随机变量序列，或$\{X,X_n,n≥1}$是正的随机变量序列使得{X_n-EX,n≥1\} 是平稳遍历的鞅差序列，记S_n=\sum\limitsⁿ_{j=1}X_j, n≥1 . 该文在条件EX=μ> 0 及0 Var(X)<∞下，证明了部分和的乘积$\prod\limits^n_{j=1}S_j/n!\mu^n$在合适的正则化因子下的某种重对数律.     

关于平稳序列中心秩顺序统计量联合分布的稳定收敛性

§1.引言 设{ξ_n}是平稳序列,ξ_1~(n)≤ξ_2~(n)≤…≤ξ_n~(n)是ξ_1,…,ξ_n的顺序统计量,则称{ξ_(kn)~(n)}{ξ_n}的具有秩序列{k_n}的顺序统计量序列。记λ_n=k_n/n和?_n={nλ_n·(1-λ_n}~(1/2),如果min{k_n,n-k_n}→∞或等价地?_n→∞就称{k_n}为变秩序列。     

E1 ο Ed型距离正则图及 Q -多项式的性质

设$\Gamma$ 是一个直径$d\geq 3$的非二部距离正则图，其特征值 $\theta_{0}>\theta_{1}>\cdots>\theta_{d}.$ 设$\theta_{1'}\in\{ \theta_{1},\theta_{d}\}, $\theta_{d'}$ 是$\theta_{1'}$ 在 $\{\theta_{1},\theta_{d}\}$中的余. 又设 $\Gamma$ 是具有性质$E_{1}\circ E_{d}=|X|^{-1}(q^{d-1}_{1d}E_{d-1}+q^{d}_{1d}E_{d})$的$E_{1}\circ E_{d}$型距离正则图,$\sigma_{0},\sigma_{1},\cdots,\sigma_{d}$,$\rho_{0},\rho_{1},\cdots,\rho_{d}$和$\beta_{0},\beta_{1},\cdots,\beta_{d}$ 分别是关于$\theta_{1'}$,$\theta_{d'}$ 和 $\theta_{d-1}$的余弦序列.利用上述余弦序列,给出了 $\Gamma$关于 $\theta_{1}$ 或$\theta_{d}$是$Q$ -多项式的充要条件.     

Estimation of optimal backward perturbation bounds for the linear least squares problem

In this paper a method of estimating the optimal backward perturbation bound for the linear least squares problem is presented. In contrast with the optimal bound, which requires a singular value decomposition, this method is better suited for practical use on large problems since it requiresO(mn) operations. The method presented involves the computation of a strict lower bound for the spectral norm and a strict upper bound for the Frobenius norm which gives a gap in which the optimal bounds for the spectral and the Frobenius norm must be. Numerical tests are performed showing that this method produces an efficient estimate of the optimal backward perturbation bound.     

关于结构KKT方程组的扰动分析

We discuss the perturbation analysis for the structured KKT systems. The methods and results of forward perturbation analysis all differ from the recent works of Gulliksson and other authors. The optimal backward perturbation results can not be deduced by the corresponding results of Sun about the KKT systems.     

ON OPTIMAL BACKWARD PERTURBATION ANALYSIS FOR THE LINEAR SYSTEM WITH BLOCK CYCLIC COEFFICIENT MATRIX

Based on the block style spectral decomposition, this paper deals with the optimal backward perturbation analysis for the linear system with block cyclic coefficient matrix.     

Condition numbers and backward perturbation bound for linear matrix equations

This paper deals with the normwise perturbation theory for linear (Hermitian) matrix equations. The definition of condition number for the linear (Hermitian) matrix equations is presented. The lower and upper bounds for the condition number are derived. The estimation for the optimal backward perturbation bound for the Hermitian matrix equations is obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

THE STRUCTURE SENSITIVITY ANALYSIS FOR TRIANGULAR SYSTEMS

Triangular systems play a fundamental role in matrix computations. It has become commonplace that triangular systems are solved to be more accurate even if they are ill-conditioned. In this paper, we define structured condition number and give structured (forward) perturbation bound. In addition, we derive the representation of optimal structured backward perturbation bound.     

Residual bounds of approximate solutions of the algebraic Riccati equation

Summary. Let approximate the unique Hermitian positive semi-definite solution to the algebraic Riccati equation (ARE) where , is stabilizable, and is detectable. Let be the residual of the ARE with respect to , and define the linear operator by By applying a new forward perturbation bound to the optimal backward perturbation corresponding to the approximate solution , we obtained the following result: If is stable, and if for any unitarily invariant norm , then Received April 28, 1995 / Revised version received August 30, 1995     

A note on the normwise perturbation theory for the regular generalized eigenproblem

In this paper, we present a normwise perturbation theory for the regular generalized eigenproblem Ax = λBx, when λ is a semi-simple and finite eigenvalue, which departs from the classical analysis with the chordal norm [9]. A backward error and a condition number are derived for a choice of flexible measure to represent independent perturbations in the matrices A and B. The concept of optimal backward error associated with an eigenvalue only is also discussed. © 1998 John Wiley & Sons, Ltd.     

Backward error and perturbation bounds for high order Sylvester tensor equation

In this article, we investigate the backward error and perturbation bounds for the high order Sylvester tensor equation (STE). The bounds of the backward error and three types of upper bounds for the perturbed STE with or without dropping the second order terms are presented. The classic perturbation results for the Sylvester equation are extended to the high order case.     

Terminal perturbation method for the backward approach to continuous time mean–variance portfolio selection

A terminal perturbation method is introduced to study the backward approach to continuous time mean–variance portfolio selection with bankruptcy prohibition in a complete market model. Using Ekeland’s variational principle, we obtain a necessary condition, i.e. the stochastic maximum principle, which the optimal terminal wealth satisfies. This method can deal with nonlinear wealth equation with bankruptcy prohibition and several examples are given to show applications of our results.     

Backward perturbation analysis for scaled total least‐squares problems

The scaled total least‐squares (STLS) method unifies the ordinary least‐squares (OLS), the total least‐squares (TLS), and the data least‐squares (DLS) methods. In this paper we perform a backward perturbation analysis of the STLS problem. This also unifies the backward perturbation analyses of the OLS, TLS and DLS problems. We derive an expression for an extended minimal backward error of the STLS problem. This is an asymptotically tight lower bound on the true minimal backward error. If the given approximate solution is close enough to the true STLS solution (as is the goal in practice), then the extended minimal backward error is in fact the minimal backward error. Since the extended minimal backward error is expensive to compute directly, we present a lower bound on it as well as an asymptotic estimate for it, both of which can be computed or estimated more efficiently. Our numerical examples suggest that the lower bound gives good order of magnitude approximations, while the asymptotic estimate is an excellent estimate. We show how to use our results to easily obtain the corresponding results for the OLS and DLS problems in the literature. Copyright © 2009 John Wiley & Sons, Ltd.