局部时的Cauchy主值的精确完全收敛性

设{X,Xn;n≥1}为i.i.d.的随机变量序列,其均值为0且EX2=1.令s={Sn}n＞0为一维随机游动,其中S0=0,Sn=n∑k=1 Xk,对n≥1.定义G(n)为随机游动局部时的Cauchy主值.本文得到了,若存在某δ1＞0,E|X|2r/(3p-4)+δ1＜∞成立,那么对4/3＜p＜2及r＞p,有limε→02(r-p)/2-p∞Σn=1nr-2/p{│G(n)│εn1/p}=2p/(r-p)πE│N│2(R-P)/2-P∞ΣK=O(-1)K(2/2K+1)2(R-P)/2-P+1.     

柯西不等式的一种构造证法

一维离散型随机变理X的方差(或数学期望)蕴含着一个不等式关系,即E(X2)≥(E(X))2(*)当且仅当X服从退化分布时(*)式中等号成立.柯西不等式设n为大于1的自然数,a1,a2,…,an与b1,b2,…,bn为实数,则(a21+a22+…+a2n)(b21+b22+…+b2n)≥(a1b1+a2b2+…+anbn)2,等号当且仅当b1=b2=…=bn时成立(当bi=0时,约定ai=0,i=1,2,…,n).     

随机场下重对数律的渐近性

设{X,Xk,k∈Zd+}是d维随机场独立同分布零均值的随机变量,β》-1/2,EX2=σ2,如果E[X2(log+|X|)α+d-1(log+log+|X|)β]《∞,则Sn=Σκ≤nXk,α》-1,β》-1/2,EX2=σ, ε(↓)σlim(2(α+d))[ε2-2(α+d)σ2(σ+d)σ2]β+1/2Σn(logㄧnㄧ)α(log logㄧnㄧ)β-ㄧnㄧP(ㄧSnㄧ≥εΓㄧnㄧlog log ㄧnㄧ)=2βσ-(d-1)!(2-(α+d))∏Γ(β+1/2), 其中Γ(·)为Gamma函数.由此回答了Gut和Spataru[4]在d=1时所提出的问题.     

可圈的一个充分条件

本文我们证明如下结果:设G=(V,E)是一个n(n≥3)阶k-连通(k≥2)图,记X1,X2,…,Xk为V的子集,X=X1∪X2∪…∪Xk.若对每个I,I=1,2,…,k,满足:对任意的u,v∈Xi,有d(u) d(v)≥n或|N(u)∪N(v)|≥n-δ或|N(u)∩N(v)|≥α,这里δ是G的最小度,α是G的独立数,则G是X-可圈的.     

局部时的Cauchy主值的精确完全收敛性

设{X,Xn;n≥1)为i.i.d.的随机变量序列,其均值为0且EX2=1.令S={Sn}n≥0为一维随机游动,其中S0=0,Sn=sum from k=1 to n Xk,对n≥1.定义G(n)为随机游动局部时的Cauchy主值.本文得到了,若存在某δ1>0,E|X|2r/(3p-4)+δ1<∞成立,那么对4/3P,有     

浅谈离散型随机变量的数学期望

当X为离散型随机变量时,如果X的取值是有限个,要求X的数学期量E(X),只要知道X的分布律就行了,但是在一些情况下,要求出X的分布律是非常困难和非常复杂的.有些时候,分布律求出来后,可按定义算出X的数学期望:E(X)一∑xipi.然而有时这个和比较难求.在以上两种情况下,我们可以利用数学期望的性质:E(X1+…+Xn)=E(X1)+…十E(Xn)把X分解为几个随机变量的和,而这几个随机变量的数学期望很容易求.一般当X表示的是与计数有关的随机变量时,大部分情形我们可以把它分解,并且是分解成0一1分布或两点分布的随机变量的和.下面通过几个例子来说明这种方法的应用.     

截断和随机乘积的渐近性质

对一列独立同分布平方可积的随机变量序列{Xn,n≥1},当随机变量的分布具有中尾分布时,讨论了其截断和Tn(a)的随机乘积的渐近正态性质,其中Tn(a)=Sn-Sn(a),n=1,2,…,Sn(a)=n∑ j=1 XjI{Mn-a＜Xj≤Mn},a为某一大于零的常数'Mn=max 1≤k≤n{Xk}.     

CONVERGENCE RATES IN THE STRONG LAWS OF NONSTATIONARY ρ-MIXING RANDOM FIELDS

1 IntroductionLet d be a positive integer, Nd be the d-dimensional lattice equipped with the coordinatewise partial order, 5. For any A C N', set SA = Z.,. X., IAI =the cardinal number of A.For anyn E Nd, let (n) = {m E N',m 5 n}, S. = s(.), Inl = I(n)l = nlnZ' nd and hull' denote the Euclidean norm. Occasionally, n,k,n, etc. will also denote positive integers, thereader will not be confused from their context. A d-dimensional discrete field of real randomvariables {Xk; k E N'} wil…     

关于诱导极限有界集的一些结果

<正> 设E_1■ E_2■ E_3…为局部凸Hausdorss线性拓扑空间序列,E_n所具有的拓扑记作ξ_n,(E,ξ)=indlim(E_n,ξ_n)为其相对于连续恒同映照id:(E_n,ξ_n)→(E_(n+1),ξ_(n+1))的Hausdorff诱导极限(见[1],p.57).显然,(E_n,ξ_n)的每个有界子集必为(E,ξ)的有界子集.Dieudonne-Schwartz定理指出:若对于n∈N,E_n闭于(E_(n+1),ξ_(n+1)),且ξ_(n+1)关于E_n的相对拓扑等于ξ_n,则E的子集B为ξ-有界,当且仅当存在n∈N使B为(E_n,     

相依假设下样本相关矩阵最大元的渐近分布

设{Xk,i;k≥1,i≥1)是一随机变量组列,令{pn;n≥1)是一正整数序列,满足c1≤n/pn≤c2,其中c1,c2是正实数.假设{Xk,i;k≥1,i≥1}满足一些相依条件,得到了Ln的渐近分布,这里Ln= ,以及表示(X1,i,…,Xn,i)'和(X1,j,…,Xn,j)'间的Pearson相关系数.     

Asymptotic Distribution of the Jump Change-Point Estimator

The asymptotic distribution of the change-point estimator in a jump changepoint model is considered.For the jump change-point model Xi =a + θI{[nTo] ＜ i ≤n} + εi,where εi (i =1,…,n) are independent ide...     

Bipartite Graphs Kn,n+r- A (|A| ≤ 3) Determined by Their Cycle Length Distributions

The cycle length distribution of a graph G of order n is a sequence (c1 (G),..., cn (G)), where ci(G) is the number of cycles of length i in G. In general, the graphs with cycle length distribution (c1(G),...,cn(G)) are not unique. A graph G is determined by its cycle length distribution if the graph with cycle length distribution (c1 (G),..., cn (G)) is unique. Let Kn,n+r be a complete bipartite graph and A(∈)E(Kn,n+r). In this paper, we obtain: Let s > 1 be an integer. (1) If r = 2s, n > s(s - 1) + 2|A|, then Kn,n+r - A (A(∈)E(Kn,n+r),|A| ≤ 3) is determined by its cycle length distribution; (2) If r = 2s + 1,n > s2 + 2|A|, Kn,n+r - A (A(∈)E(Kn,n+r), |A| ≤ 3) is determined by its cycle length distribution.     

由圈长分布确定的二部图~$K_{n,n r}-A\ (|A|\leq 3)$

The cycle length distribution of a graph G of order n is a sequence （c1 （G）,…, cn （G））, where ci （G） is the number of cycles of length i in G. In general, the graphs with cycle length distribution （c1（G） ,…,cn（G）） are not unique. A graph G is determined by its cycle length distribution if the graph with cycle length distribution （c1 （G）,…, cn （G）） is unique. Let Kn,n＋r be a complete bipartite graph and A lohtaib in E（Kn,n＋r）. In this paper, we obtain： Let s 〉 1 be an integer. （1） If r = 2s, n 〉 s（s - 1） ＋ 2｜A｜, then Kn,n＋r - A （A lohtain in E（Kn,n＋r）,｜A｜ ≤ 3） is determined by its cycle length distribution; （2） If r = 2s ＋ 1,n 〉 s^2 ＋ 2｜A｜, Kn,n＋r - A （A lohtain in E（Kn,n＋r）, ｜A｜ ≤3） is determined by its cycle length distribution.     

代數拓撲學中(μ,△,γ)-系統的正則同模論Ⅰ

<正> 設K與L為拓撲空間,又設f:K→L為連續映像.由f導出了準同模對應f~n:H~n(L,G)→H~n(K,G),n=1,2,…,其中H~n(L,G),H~n(K,G)表示上同調羣,而G表示係數環或域以γ_p~n(K)或者     

Characterizations of the uniform distribution via sample spacings and nonlinear transformations

We prove that an absolutely continuous probability distribution with compact support is uniformly distributed if and only if the mean sample spacings resulting from a random sample of size N are all equal for every integer N. We also present a related characterization of uniformity using nonlinear transformations. We discuss potential applications of these results to hypothesis testing and to testing the effectiveness of different random number generators.     

偶图$K_{n,n+7}-A(|A|\leq3)$的圈长分布唯一性

阶为$n$的图$G$的圈长分布是序列($c_1,c_2,\ldots,c_n$), 其中$c_i$是图$G$中长为$i$的圈数.本文得到如下结果: 设$A\subseteq E(K_{n,n+7})$,在以下情况, 图 $G$ 由其圈长分布唯一确定.(1) $G=K_{n,n+7}$(n\geq10)$;(2) $G=K_{n,n+7}-A$ $(|A|=1,n\geq12)$;(3)$G=K_{n,n+7}-A$(|A|=2,n\geq14)$;(4)$G=K_{n,n+7}-A$ $(|A|=3     

关于B-凸空间及其上黎斯算子West分解

给出 Ｂａｎａｃｈ空间列｛Ｘｉ｝ｉ＝１∞的 ｌｐ乘积Ｂ－凸的特征刻划, 证明Ｂ－凸空间上的每个黎斯算子可Ｗｅｓｔ分解,即分解成一个紧算子和一个拟幂 零算子的和．     

球舆特殊多面體有同模的同倫羣論

<正> 球上同倫羣的研究,是近代拓撲學中一種最重要的工作,三、四年來,這工作發展得尤其迅速,但是像同緯映像術E:π_q(S~n)→π_(q+1)(S~(n+1))這樣,雖然是很重要的一種工具,而E的像和E的核,除有限種情况外,長久沒有一種表示     

Multivariate dependence of spacings of generalized order statistics

Multivariate dependence of spacings of generalized order statistics is studied. It is shown that spacings of generalized order statistics from DFR (IFR) distributions have the CIS (CDS) property. By restricting the choice of the model parameters and strengthening the assumptions on the underlying distribution, stronger dependence relations are established. For instance, if the model parameters are decreasingly ordered and the underlying distribution has a log-convex decreasing (log-concave) hazard rate, then the spacings satisfy the MTP₂ (S- MRR₂) property. Some consequences of the results are given. In particular, conditions for non-negativity of the best linear unbiased estimator of the scale parameter in a location-scale family are obtained. By applying a result for dual generalized order statistics, we show that in the particular situation of usual order statistics the assumptions can be weakened.     

风险模型中重尾随机变量和的若干大偏差结果

进一步研究随机变量部分和与随机和的大偏差,其中S(n)=∑ni=1Xi,S(t)=∑N(t)i=1Xi(t>0).{Xn,n≥1}是一个独立同分布的随机变量(未必是非负的)序列具有共同的分布F(定义于R上)和有限期望μ=EX1.{N(t),t≥0}是一个非负的整数值的随机变量的更新计数过程且与{Xn,n≥1}相互独立.本文在假定F∈C条件下,进一步推广并改进了由Klüppelberg等和Kaiw等人给出的一些大偏差结果.这些结果可应用到某些金融保险方面的一些特定的问题中去.