取值于Banach空间的L~1极限鞅及其性质

本文给出了Banach空间中随机变量列弱L~1收敛的定义,讨论了L~1极限鞅的收敛性、Riesz分解等等。 下面所言积分均为Bochner积分;B表Banach空间,1·1表B中范数,B~*表共轭空间;取值于B中的随机变量(即强可测函数)简称为B值随机变量;{n≥1)是一列单调上升σ代数。设(Ω,P)是一概     

同时CHEBYSHEV逼近

设Ω是紧 Hausdorff 空间,X 是 Bauach 空间,C(Ω,X)表示定义在Ω上取值于 X中的连续函数组成的线性空间,在 C(Ω,X)上赋予范数。     

条件期望算子与向量值Orlicz空间的紧性

设(Ω,∑,μ)是无原子有限测度空间,φ(t)是 N-函数,φ的余函数为Ψ.我们讨论的是函数空间 L_(?)(μ,X),其中的每个元 f 是定义在 Ω上,取值于 Banach 空间 X,关于μ 强可测的函数并且有某个 k>0,使 integral from Ω Φ(k~(-1)‖f(ω)‖)dμ<∝.把仅在零测度集上不同的函数视为同一元,并且令     

抽象L~1-空间上的Radon-Nikodym性质

设(Ω,F,P)为非平凡概率空间,(F_n,n≥1)为一单调不降的F的子σ-代数序列,B为Banach格,表示B中的范数.称X:Ω→B为B值随机元,若X关于F强可测.称B值序列(X_n,F_n,n≥1)是适应可积的,若X_n关于F_n强可测且E X_n<∞(n≥1).对B内的元x,记x~+=x∨0,x~-=x∧0,x=x~(+)+x~-,|x|=x~+-x~-.B内的元x,y,若|x|≤|y|,则x≤y.     

Banach空间的光滑性与B值随机变量列的收敛性

本文研究了Banach空间的光滑性与B值随机变量收敛性之间的关系,得到了B值随机变量列的几个收敛定理,其中有些推广了Woyczyski在[15]、[16]中的结果,此外,还讨论了UMD空间中的部分收敛性问题。 本文所言积分均为Bochner积分;B表Banach空间,1·1表B中的范数,B~*表共轭空间;R_ [0,∞);取值于B空间的随机变量(即强可测函数)简称B值随机变量,类似还有B值鞅等等;r.v.表随机变量,r.v.s.表随机变量列。     

多目标最优停止与约束最优停止

最优停止理论作为概率论的一个部分,自1960年以来处于迅速发展之中,比较系统的著作当推〔1〕,〔2〕,最优停止理论的一般提法如下: 我们假设给出i)概率空间(Ω,P),ii)一列递增的的子σ代数族,iii)一个关于(_n)适应可测的随机变量序列(X_n),一般我们称为报酬序列。取值1,2,…,+∞的随机变量t=t(ω),称为停时是指对任何n,{t,(ω)=n}∈,如果停时t满足t<∞a.s.,则称它为停止变量或停止规则,定义随机序列{X_n,_n}~∞的值V为supEX_t,其中C= {t:t为停止变量,EX_t<∞},最优停止理论所要讨论的是下列问题:     

随机算子方程一般随机解的存在性

§1.引言 设(Ω,(?),P)为一完备概率测度空间,(X,B(X))、(Y,B(Y))为二可测空间,其中(X,‖·‖)、(Y,‖·‖)为可分Banach空间,B(X)与B(Y)分别表示X与Y的开子集所产生的Borel-σ-代数。映射x:Ω→X称为可测的,如果对任B∈(?)(X),考虑带随机参数的方程     

方向数据密度核估计的对数律

设X为取值于k维单位球面上的单位随机向量,具有概率密度函数f(x),X_1,…,X_n为X的n个i.i.d.的观察,讨论f(x)具有形式的核估计,其中K为定义于[0,+∞]上的非负核函数,ω_k为Ω_k上的Lebesque测度,本文建立了fn(x)的对数律,并给出了fn(x)的一致强相合速度。     

一类特殊Beatty序列中的素因子问题

研究了数论函数Ω和ω取值于一类特殊的非齐次Beatty序列[αn+β](n=1,2,…)的问题.特别地,证明了渐近公式∑ω([αn+β)=N log log N+O(N(log log N) )以及∑(一1)Ω(αn+β)=O( n/(log N 1/2)),其中α,β∈R,n∈Z+,α>0是型为1的无理数,Ω(k)和ω(k)表示整数k(≠0)的素因子个数(Ω记重数,ω不计重数).     

马氏链的离散分布(Ⅱ)

设X(ω)={x(t,ω), t≥0}是定义在完备概率空间(Ω,,p)上的马氏链。其状态空间1={0,1,2,…}。如不作特别声明都假定X(ω)具有标准转移矩阵,完全可分,Borel可测,状态稳定。令     

关于随机赋范空间与随机内积空间的某些基本理论(英文)

首先提出随机度量空间定义的另一个提法,这提法不仅等价于原始的定义而且也使随机度量空间自动归入广义度量空间的框架,也考虑了关于拓扑结构的某些新的问题;循着同样的思路,对随机赋范空间的定义也作了新的处理并同时简化了随机赋范模的定义．其次本文也证明了一个Ｅ－范空间的商空间等距同构于一个典型的Ｅ－范空间;进一步,在概率赋范空间的框架下证明了一个概率赋伪范空间是伪内积生成空间的充要条件是它等距同构于一个Ｅ－内积空间,这回答了Ｃ．Ａｌｓｉｎａ与Ｂ．Ｓｃｈｗｅｉｚｅｒ等人新近提出的公开问题．最后,本文转向了它的中心部分──关于随机内积空间的研究,对随机内积空间中的特有且复杂的正交性作较系统的讨论,论证了只有几乎处处正交性才是唯一合理的正交性概念,在此基础上本文尤其将Ｇ．Ｓｔａｍｐａｃｃｈｉａ的在众多学科中都有多种用途的一般投影定理（或称变分不等式解存在性定理）以适当形式推广到完备实随机内积模上．     

The dual of C ps (X)

This is a study of the dual space of continuous linear functionals on the function space C_ps(X) with a natural norm inherited from a larger Banach space. Here ps denotes the pseudocompact-open topology on C(X), the set of all real-valued continuous functions on a Tychonoff space X. The lattice structure and completeness of this dual space have been studied. Since this dual space is inherently related to a space of measures, the measure-theoretic characterization of this dual space has been studied extensively. Due to this characterization, a special kind of topological space, called pz-space, has been studied. Finally the separability of this dual space has been studied.      

Norm attaining operators

Every Banach space is isomorphic to a space with the property that the norm-attaining operators are dense in the space of all operators into it, for any given domain space. A super-reflexive space is arbitrarily nearly isometric to a space with this property.     

受限制多项式插值及在构造形函数空间中的应用

1引言 G.Strang指出：有限元法的新思想在于试控函数的选择，目标是选择这样的分片多项式，它们被少数几个方面的节点值确定，并仍具有我们需要的连续性和逼近度。受限制多项式插值空间就是这样一类空间，在P.G.Ciarlet~[4]的书中有较多的介绍，采用的方法是通过约束条件来决定试验空间，但正如[1]中指出的，这样约束条件欠直观，且容易产生一些不确     

A note on the space of fuzzy measurable functions for a monotone measure

In this paper, we give a necessary and sufficient condition to guarantee that the space of all finite measurable functions for a monotonic measure is a topological vector space with a countable local base and in this space convergence with respect to this topology is equivalent to the convergence in measure.     

两点齐性的Finsler流形

该文证明任何一个两点齐性的Finsler流形一定是黎曼流形．证明过程中作者将泛函分析中经典的Mazur定理推广到不一定是绝对齐次的Minkowski空间上．     

两点齐性的 Finsler 流形

该文证明任何一个两点齐性的 Finsler 流形一定是黎曼流形. 证明过程中作者将泛函分析中经典的Mazur 定理推广到不一定是绝对齐次的 Minkowski 空间上.     

Geometry of the structure of linear complements

Two geometries can be considered in the structure of linear complements: an affine spine space and an affine space. An affine spine space arises from a space of pencils. In terms of this geometry an affine partial line space may be defined. It is extensible to the affine space. Automorphisms of the affine spine space are automorphisms of appropriate affine space.     

Strong convergence theorem by shrinking projection method for new nonlinear mappings in Banach spaces and applications

In this paper, we introduce the concept of a new nonlinear mapping called demigeneralized in a Banach space. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common fixed point for a family of the new nonlinear mappings in a Banach space. We apply this result to obtain new strong convergence theorems in a Hilbert space and a Banach space, respectively.     

Extension of an abstract attainability problem with the use of the stone representation space

We consider an attainability problem in a complete metric space on values of an objective operator h. We assume that the latter admits a uniform approximation by mappings which are tier with respect to a given measurable space with an algebra of sets. Let asymptotic-type constraints be defined as a nonempty family of sets in this measurable space. We treat ultrafilters of the measurable space as generalized elements; we equip this space of ultrafilters with a topology of a zero-dimensional compact (the Stone representation space). On this base we construct a correct extension of the initial problem, realizing the set of attraction in the form of a continuous image of the compact of feasible generalized elements. Generalizing the objective operator, we use the limit with respect to ultrafilters of the measurable space. This provides the continuity of the generalized version of h understood as a mapping of the zero-dimensional compact into the topological space metrizable with a total metric.