随机变量部分和的矩不等式

研究由随机变量和的M-Z-B型不等式导出Rosenthal型不等式的条件 ,并对较广泛的一类随机变量证明了M-Z-B型不等式 ,从而获得多种类型随机变量序列的Rosenthal型不等式     

ND序列部分和的大偏差和强收敛性

利用ND随机变量序列的矩不等式、极大值不等式以及随机变量的截尾方法,重点研究了ND随机变量序列部分和的大偏差结果和强收敛性,推广了文献中一些相依随机变量序列的若干相应结果.     

随机线性不等式组的确定性等价式

在大量的决策问题中，经常会出现含有随机变量的不等式或不等式组。把这类含有随机变理的模型转化成确定性的模型是解决问题的重要途径。它们在随机控制和不完全信息群体决策随机决策问题中起着重要的作用。因此，如何将随机不等林或随机不等式组转化为相应的确定性等价式的问题受到人们的关注。本文对含有确定分布的随机变量的线性不等式组，就其相应的概率表达式作出分类，并根据其左端系数矩阵和右端向量含有随机因素的情形分别进行讨论，系统地导出了它们相应的确定性等价式。     

NA随机变量序列的最大部分和不等式及有界重对数律

本文给出了NA随机变量序列关于最大部分和的概率不等式及矩不等式,并获得了NA随机变量序列的Teicher型和Egorov型有界重对数律等.     

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本文给出了上期望空间中独立随机变量部分和的最大不等式、指数 不等式、Marcinkiewicz-Zygmund不等式. 并且应用指数不等式和Marcinkiewicz-Zygmund不等式 研究了随机变量部分和序列完备收敛的性质.     

行内负相关随机变量组列的完全收敛性

运用NA随机变量的矩不等式以及邵启满给出的关于NA随机变量概率不等式,在NA的情况下给出了类似与Chen(2005),Sung(2005)关于行内独立随机变量完全收敛性的结论.同时在给出的条件比上述作者的结论条件更加弱.     

对称随机变量部分和的概率不等式

在对称随机变量分布函数关于原点的值大于或等于二分之一的基础上,阐明对称随机变量的部分和仍是对称随机变量,进一步,给出关于对称随机变量序列部分和的概率不等式.     

ρ-混合序列加权和的完全收敛性

本文研究ρ-混合随机变量序列的加权和.利用文献[10]的矩不等式,在勿需控制混合系数的情况下,得到了完全收敛的充分条件,对“同分布”情形,得到了完全收敛的必要条件,推广了文献[8,10]中的有关结果.     

NA随机变量阵列的完全矩收敛性

利用NA随机变量的矩不等式和截尾方法,研究了NA随机变量阵列的完全矩收敛性,给出了证明NA随机变量阵列完全矩收敛性的一些充分条件.所得结果推广了已有文献关于NA随机变量的相应结果.     

END序列加权和的完全收敛性

该文把Sung~([1])的一个关于同分布NA随机变量序列加权和最大值完全收敛性结果部分推广到了END随机变量序列情形.由于已有文献所用的工具是部分和最大值指数型不等式或部分和最大值Rosenthal型矩不等式,而对于END而言相应的不等式是否成立至今未知,因此原有的证明方法已失效.该文将应用END随机变量序列部分和的Rosenthal型矩不等式,结合三段截尾法,获得了理想的结果.该文的证明方法不同于已有的结果.     

Solving a nonlinear inverse Robin problem through a linear Cauchy problem

ABSTRACT

Considered in this paper is an inverse Robin problem governed by a steady-state diffusion equation. By the Robin inverse problem, one wants to recover the unknown Robin coefficient on an inaccessible boundary from Cauchy data measured on the accessible boundary. In this paper, instead of reconstructing the Robin coefficient directly, we compute first the Cauchy data on the inaccessible boundary which is a linear inverse problem, and then compute the Robin coefficient through Newton's law. For the Cauchy problem, a parameter-dependent coupled complex boundary method (CCBM) is applied. The CCBM has its own merits, and this is particularly true when it is applied to the Cauchy problem. With the introduction of a positive parameter, we can prove the regularized solution is uniformly bounded with respect to the regularization parameter which is a very good property because the solution can now be reconstructed for a rather small value of the regularization parameter. For the problem of computing the Robin coefficient from the recovered Cauchy data, a least square output Tikhonov regularization method is applied to Newton's law to obtain a stable approximate Robin coefficient. Numerical results are given to show the feasibility and effectiveness of the proposed method.     

目标函数系数与约束右端项同时变化的灵敏度分析

灵敏度分析应用很广,但是人们对灵敏度的讨论往往局限于单个参数发生变化对求解结果的影响.本文主要讨论目标函数系数C和约束右端项b两个参数同时改变对最优基、最优解及目标值的影响以及最优解发生变化时,如何求出新的最优解.     

关于PSD迭代法收敛的充分必要性定理

本文在线性方程组系数矩阵A为相容次序矩阵及A的Jacobi迭代矩阵的特征值μ_j均为实数且μ_j~2<1的条件下,得出了PSD迭代法收敛的充分必要性定理,并由此而得到了一个易于判别的PSD法收敛性定理。     

二阶变系数椭圆型微分方程谱方法的后验误差估计

As to the posteriori error of spectral method for second order elliptic differential equation of variable coefficient,we construct two easy solvable differential equations of constant coefficient. Among the two energy norms of the solutions of two differential equations, one is larger than the energy norm of exact error ,another is smaller than the energy norm of exact error, and the two energy norms of the solutions are of same order.     

Anticipating Stochastic Differential Equations of Stratonovich Type

We prove the existence and uniqueness of Stratonovich stochastic differential equations where the coefficients and the initial condition may depend on the whole path of the driving Wiener process. Our main hypothesis is that the diffusion coefficient satisfies the Frobenius condition. The solution is given in terms of solutions of ordinary differential equations and the Wiener process. We use this representation to study properties of the solution. Accepted 3 April 1996     

变系数模型变窗宽局部M-估计的相合性

用变窗宽局部M-估计对变系数模型的系数函数进行估计,得到了估计的相合性和渐近正态性.所采用的方法继承了局部多项式回归的优点并且克服了最小二乘方法缺乏稳健性的缺点.变窗宽的使用提高了局部M-估计的可塑性,并使得它们能成功地处理空间非齐性曲线、异方差性及非均匀设计密度.     

删失数据下半变系数模型估计的渐近正态性

半变系数回归模型是变系数回归模型的有效推广,已获得了广泛的应用. 本文在响应变量随机删失下对其进行讨论,给出常系数和函数系数的估计, 并证明了该估计的渐近正态性.     

几个关于Mercier恒等式的推广

本文建立了几个包含Gauss二项系数的恒等式，这些结果推广了几个Mercier的结果。     

Boundary-domain integral equations for the diffusion equation in inhomogeneous media based on a new family of parametrices

ABSTRACT

A mixed boundary value problem (BVP) for the diffusion equation in non-homogeneous media partial differential equation is reduced to a system of direct segregated parametrix-based boundary-domain integral equations (BDIEs). We use a parametrix different from the one employed by Mikhailov [Localized boundary-domain integral formulations for problems with variable coefficients. Eng Anal Bound Elem. 2002;26:681–690], Mikhailov and Portillo [A new family of boundary-domain integral equations for a mixed elliptic BVP with variable coefficient. In: Paul Harris, editor. Proceedings of the 10th UK conference on boundary integral methods. Brighton: Brighton University Press; 2015. p. 76–84] and Chkadua, Mikhailov, Natroshvili [Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. I: equivalence and invertibility. J Integral Eqs Appl. 2009;21:499–543]. We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed.