强相依高斯序列超过数点过程与部分和的联合渐近分布

（Ｘｎ）为标准化平稳高斯序列,ｐｎ＝ＥＸ１Ｘｎ＋１,Ｎｎ为Ｘ１,Ｘ２,…,Ｘｎ对水平ｕｎ＝ｘ／ａｎ＋ｂｎ的超过数形成的点过程,Ｍｎ＾（ｋ）为Ｘ１,Ｘ２,…,Ｘｎ的第ｋ个最大值,Ｓｎ＝（ｎ）∑（ｉ＝１）Ｘｉ,ｐｎｌｏｇｎ→ｒ∈（０,∞）时,得到Ｎｎ与Ｓｎ、Ｍｎ＾（ｋ）与Ｓｎ的联合渐近分布。     

强相依非平稳高斯序列超过数点过程与部分和的联合渐近分布

设{Xi}∞i=1是标准化强相依非平稳高斯序列,记Sn=∑Xi,σn=√var(Sn),Mktn为X1,X2,…,Xtn的第k个最大值,Ntn为X1,X2,…,Xtn对水平μn(x)的超过数形成的点过程,tn是-列单调增加的正整数列,在一定条件下得到Ntn与Sn/σn,Mktn与Sn/σn的联合渐近分布.     

具有随机足标的弱相依高斯序列最大值的极限分布

设ξ1,ξ2,…为标准化的平稳高斯序列.Mn=max.ξi,协方差Υn=Cov(ξ1,ξn+1)=E(ξ1ξn+1).{N(n)}为-列取正整数的随机变量,满足 0,n→∞.在条件Υnlogn→0,n→∞之下,给出了 MN(n)的极限分布.     

平稳正态序列超过数点过程与部分和的渐近联合分布

{Xi}为平稳正态序列,具有EX1=0,EX12=1,ρn=EX1Xn 1.对于水平un= ,记在 的条件下,得到了Nn(B)与Sn的渐近联合分布,同时也给出了极值与Sn的渐近联合分布.     

一类相依正态序列超过数点过程的渐近分布

{X_n,n≥1}为存在样本缺失的标准化平稳正态序列,相关系数r_n=EX_1X_(1+n).(?)_n与(?)_n分别为观测到与未观测到的子样形成的超过数点过程.令N_n=(?)_n+(?)_n.本文研究r_nln→ρ∈[0,∞)时超过数点过程N_n,(?)_n与(?)_n的弱收敛性及顺序统计量的联合渐近分布.     

强相依高斯序列的最大值与和的联合渐近分布

{X_n,n≥1)是标准高斯序列,T_(ij)=cov(X_i,X_j)。本文在强相依条件rijlog(j-i)→r∈(0,∞)(j-i→ ∞)下,得到了高斯序列的最大值M_n与标准化部分和S_n=sum from i=1 to n(X_i/(E(sum from i=1 to n X_i)~2)/(1/2))     

非平稳高斯序列超过数点过程与部分和的联合渐近分布

设$\{X_{i}\}^{\infty}_{i=1}$是标准化非平稳高斯序列, $N_{n}$为$X_{1},X_{2},\cdots,X_{n}$对水平$\mu_{n}(x)$的超过数形成的点过程, $r_{ij}=\ep X_{i}X_{j}$, $S_{n}=\tsm_{i=1}^{n}X_{i}$. 在$r_{ij}$满足一定条件时, 本文得到了$N_{n}$与$S_{n}$的渐近独立性.     

一类非平稳高斯序列超过数点过程与和的渐近性

设{X_i}_(i=1)~∞是标准化非平稳高斯序列,N_n为X_1,X_2,…,X_n依次对水平μ_(n1),μ_(n2),…,μ_(nn)的超过数形成的点过程.记Υ_(ij)=X_iX_j,S_n=■X_i.当Υ_(ij)满足一定条件时,证明了N_n依分布收敛到Poisson过程,且N_n与S_n渐近独立.     

含趋势项强相依非平稳序列的两个重要分布

{ηn}为平稳标准化正态序列,相关系数r|t-j|=Cov(ηu,ηj),若rnlogn→∞时,Leadbetter[1]等得到了序列最大值的渐近分布.本文考虑非平稳带有趋势项序列{ηn},得到了序列最大值的渐近分布和最大值与部分和的联合渐近分布.     

一类多维参数高斯过程的弱逼近

本文研究了一类多维参数高斯过程的弱极限问题.在一般情况下,利用泊松过程得到了此类过程的弱极限定理,此多维参数高斯过程可表示为确定的核函数关于维纳过程的随机积分,且包含多维参数的分数布朗运动.     

关于任意随机可积序列的一个强收敛定理

本文研究了可积随机适应序列强收敛定理的问题.利用构造截尾停时以及鞅差序列的方法,获得了一类任意积随机适应序列的强收敛定理,推广了若干已知的结果.     

赋序列范数的矢值Banach序列空间的强U-点和暴露点

刻划了赋序列范数的矢值Banach序列空间$ss(E)$的强U-点和暴露点,给出了它们的判据.     

STRONG CONVERGENCE OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR A CLASS OF SEMILINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH MULTIPLICATIVE NOISE

This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations(SPDEs)with multiplicative noise.The nonlinearity in the diffusion term of the SPDEs is assumed to be globally Lipschitz and the nonlinearity in the drift term is only assumed to satisfy a one-sided Lipschitz condition.These assumptions are the same ones as the cases where numerical methods for general nonlinear stochastic ordinary differential equations(SODEs)under"minimum assumptions"were studied.As a result,the semilinear SPDEs considered in this paper are a direct generalization of these nonlinear SODEs.There are several difficulties which need to be overcome for this generalization.First,obviously the spatial discretization,which does not appear in the SODE case,adds an extra layer of difficulty.It turns out a spatial discretization must be designed to guarantee certain properties for the numerical scheme and its stiffness matrix.In this paper we use a finite element interpolation technique to discretize the nonlinear drift term.Second,in order to prove the strong convergence of the proposed fully discrete finite element method,stability estimates for higher order moments of the H1-seminorm of the numerical solution must be established,which are difficult and delicate.A judicious combination of the properties of the drift and diffusion terms and some nontrivial techniques is used in this paper to achieve the goal.Finally,stability estimates for the second and higher order moments of the L2-norm of the numerical solution are also difficult to obtain due to the fact that the mass matrix may not be diagonally dominant.This is done by utilizing the interpolation theory and the higher moment estimates for the H1-seminorm of the numerical solution.After overcoming these difficulties,it is proved that the proposed fully discrete finite element method is convergent in strong norms with nearly optimal rates of convergence.Numerical experiment results are also presented to validate the theoretical results and to demonstrate the efficiency of the proposed numerical method.     

UNIFORM CONVERGENCE AND SEQUENCE OF MAPS ON A COMPACT METRIC SPACE WITH SOME CHAOTIC PROPERTIES

Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f ： X →X of a sequence of continuous topologically transitive （in strongly successive way） functions fn ： X →X, where X is a compact interval. Surprisingly, we find that the uniform limit function is chaotic in the sense of Devaney. Lastly, we give an example to show that the denseness property of Devaney＇s definition is lost on the limit function.     

CONVERGENCE OF IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

The purpose of this article is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this article extend and improve the corresponding results of [1, 2, 4-9, 11-15].