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1.
负相依随机变量的自正则化中心极限定理与部分和的方差估计 总被引:1,自引:0,他引:1
§ 1 IntroductionWe firstintroduce some concepts.Random variables X and Y are called negative dependent ( ND) if for any pair ofmonotonically non-decresing functions f and g,Cov{ f( X) ,g( Y) }≤ 0 .Clearly itis equivalenttoP( X≤ x,Y≤ y)≤ P( X≤ x) P( Y≤ y)for all x,y∈R.A random sequence{ Xi,i≥ 1 } is said to be negative quadrant dependent( NQD) if any pairof variables Xi,Xj( i≠j) are ND.A sequence of random variables{ Xi,i≥ 1 } is said to be linear negative quadrand depend… 相似文献
2.
Let(X,‖·‖ ) be a normed space.Let S(X) ={ x∈X:‖x‖ =1 } and B(X) ={ x∈X:‖ x‖≤ 1 } be the unit sphere and unit ball of X,respectively.In 1 990 ,Gao andLau[1 ] introduced the following definition. Definition The Parameter CJ(X) of a normed space X,which will be called a non-square constant in the sense of James in this paper,is defined byCJ(X) =sup{‖ x + y‖∧‖ x -y‖ :x,y∈ S(X) } .The nonsquare constant CS(X) of a normed space X in the sense of Schaffer is definedbyC… 相似文献
3.
设G为局部紧交换群,为G的对偶群.设S_1(G)与S_2(G)是G上的Segal代数.记S_1(G)到S_2(G)的乘子全体为M(S_1,S_2).本文主要证明了下面两个结果: 1.T∈M(S,L~1)当且仅当存在唯一的σ∈E_s~*使得Tf=σ*f f∈S(G),且‖T‖=‖σ‖E_s~*. 2.设S_2(G)S_1(G)且‖f‖S_1≤‖f‖S_2,f∈S_2(G).若T∈M(S_1,S_2),则存在唯一的G上有界连续函数φ使得其中是f的Fourier变换. 相似文献
4.
Let(X,)be a measurable space,and,=σ-field generated by {x|x∈X},where x={A∈ |x∈A}.(Y,)another measurable space,let ρ(X, Y,)={∈ |§ be measurable}.∈ρ(X,Y,),we define ()(y)=~(-1)(y),y∈y. Defination 1.T is an index set,f:{0,1}~T→{0,1},then,O~T:( (Y)~x)~T→ (Y)~x is called the operation derived from f if for any { }_(t∈T)∈((Y)~x)~Tand any(x,y)∈X×Y,it holds 相似文献
5.
蒋烨 《高校应用数学学报(英文版)》2003,18(2):200-208
§ 1 IntroductionA finite family of random variables { Xi,1≤ i≤ n} is said to be negatively associated(NA) is for every pair of disjointsubsets A1 and A2 of{ 1 ,2 ,...,n} ,Cov{ f1 (Xi,i∈ A1 ) ,f2 (Xj,j∈ A2 ) }≤ 0 ,(1 .1 )whenever f1 and f2 are coordinatewise increasing and the covariance exists.An infinitefamily is negatively associated ifevery finite subfamily is negatively associated.This defini-tion was introduced by Alam and Saxena[1 ] and Joag-Dev and Proschan[2 ] .As pointed… 相似文献
6.
设E是任意一个非空的闭实数集(mod 2π),ρ(θ)是E上一个上半连续的有界正值函数(0<ρ(θ)相似文献
7.
K是Banach空间E的一个非空闭凸子集,T:K→K是一个广义Lipschitz伪压缩映射.对Lipschitz强伪压缩映射f:K→K和x_1∈K,序列{x_n}由下式定义:x_n+1=(1-α_n-β_n)x_n+α_nf(x_n)+β_nTx_n.在{α_n}与{β_n}满足合适条件的情况下,每当{z∈K;μ_n‖x_n-z‖~2=inf_(y∈K)μ_n‖x_n-y‖~2}∩F(T)≠φ时,{x_n}强收敛到T的某个不动点x~*. 相似文献
8.
Yu Ping SONG 《数学学报(英文版)》2014,(1)
An umbilical free oriented hypersurfacex:M→Rnwith non-zero principal curvatures is called a Laguerre isoparametric hypersurface if its Laguerre form C=i Ciωi=iρ1(Ei(logρ)(r ri)Ei(r))ωi vanishes and Laguerre shape operator S=ρ1(S 1 rid)has constant eigenvalues.Hereρ=i(r ri)2,r=r1+r2+···+rn 1n 1is the mean curvature radius andSis the shape operator ofx.{Ei}is a local basis for Laguerre metric g=ρ2III with dual basis{ωi}and III is the third fundamental form ofx.In this paper,we classify all Laguerre isoparametric hypersurfaces in Rn(n3)with two distinct non-zero principal curvatures up to Laguerre transformations. 相似文献
9.
Let G(V, E) be a graph. A k-adjacent vertex-distinguishing equatable edge coloring of G, k-AVEEC for short, is a proper edge coloring f if (1) C(u)≠C(v) for uv ∈ E(G), where C(u) = {f(uv)|uv ∈ E}, and (2) for any i, j = 1, 2,… k, we have ||Ei| |Ej|| ≤ 1, where Ei = {e|e ∈ E(G) and f(e) = i}. χáve (G) = min{k| there exists a k-AVEEC of G} is called the adjacent vertex-distinguishing equitable edge chromatic number of G. In this paper, we obtain the χáve (G) of some special graphs and present a conjecture. 相似文献
10.
Let S belong to Zn-{0}.The circulant digraph DCn(S) is a directed graph with vertex set Zn and are set {(i,i s):i∈Zn,s∈S},A.Adam conjectured that DCn(S)≌DCn(T) if and only if T=uS for some unit u mod n.In this paper we prove that the conjecture is true if S is a minimal generating set of Zn and thus determine the full automorphism groups of such digraphs.The methods we employ are new and easy to be understood. 相似文献
11.
Convergence rates in the strong laws of asymptotically negatively associated random fields 总被引:15,自引:0,他引:15
ZhangLixin WangXiuyun 《高校应用数学学报(英文版)》1999,14(4):406-416
In this paper, a notion of negative side p-mixing (p -mixing) which can be regardedas asymptotic negative association is defined, and some Rosenthal type inequalities for p -mix-ing random fields are established. The complete convergence and almost sure summability onthe convergence rates with respect to the strong law of large numbers are also discussed for p--mixing random fields. The results obtained extend those for negatively associated sequences andp“ -mixing random fields. 相似文献
12.
Inequalities of Maximum of Partial Sums and Weak Convergence for a Class of Weak Dependent Random Variables 总被引:11,自引:0,他引:11
Jiang Feng WANG Feng Bin LU 《数学学报(英文版)》2006,22(3):693-700
In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for ρ^- -mixing random fields. As its applications we get the Hájeck -Rènyi inequality and weak convergence of sums of ρ^- -mixing sequence. These results extend related results for NA sequence and p^* -mixing random fields, 相似文献
13.
张涤新 《中国科学A辑(英文版)》2002,45(2):223-232
Assume that {Xn} is a strictly stationary β-mixing random sequence with the β-mixing coefficient βk = O(k-r), 0 < r ≤1. Yu (1994) obtained convergence rates of empirical processes of strictly stationary β-mixing random sequence indexed by bounded classes of functions. Here, a new truncation method is proposed and used to study the convergence for empirical processes of strictly stationary β-mixing sequences indexed by an unbounded class of functions. The research results show that if the envelope of the index class of functions is in Lp, p > 2 or p > 4, uniform convergence rates of empirical processes of strictly stationary β-mixing random sequence over the index classes can reach O((nr/(l+r)/logn)-1/2) or O((nr/(1+r)/ log n)-3/4) and that the Central Limit Theorem does not always hold for the empirical processes.`` 相似文献
14.
By some moment inequalities for α-mixing random variables, we prove the Bahadur representation of sample quantiles under very weak α-mixing coefficients. As application, the uniformly asymptotic normality is derived, the rate of which is near to n
−1/6 under the given conditions. 相似文献
15.
Curtis Miller 《Journal of Theoretical Probability》1994,7(4):867-882
This paper generalizes results by Bradley.(3) Suppose that for 1=1,2,...X
k
1
:k
d
is a centered, weakly stationary *-mixing random field, and suppose liml Cov(X
0
1
,x
k
1
) exists, anyk
d
. Then the successive spectral densities converge uniformly to a continuous function. For a sequence of strictly stationary random fields that are uniformly *-mixing and satisfy a indeberg condition, a CLT is proved for sequences of sums from the fields. This result is then applied: given a centered strictly stationary *-mixing random field whose probability density and joint densities are continuous, then a kernel estimator for the probability density obeys the CLT. 相似文献
16.
Summary. We consider the Cauchy problem for the mass density ρ of particles which diffuse in an incompressible fluid. The dynamical
behaviour of ρ is modeled by a linear, uniformly parabolic differential equation containing a stochastic vector field. This
vector field is interpreted as the velocity field of the fluid in a state of turbulence. Combining a contraction method with
techniques from white noise analysis we prove an existence and uniqueness result for the solution ρ∈C
1,2([0,T]×ℝ
d
,(S)*), which is a generalized random field. For a subclass of Cauchy problems we show that ρ actually is a classical random field,
i.e. ρ(t,x) is an L
2-random variable for all time and space parameters (t,x)∈[0,T]×ℝ
d
.
Received: 27 March 1995 / In revised form: 15 May 1997 相似文献
17.
In the present paper, the embedding problem is considered for number fields with p-groups whose kernel is either of two groups
with two generators α and β and with the following relations: (1) αρ=1, αρ=1, [α,β,β]=1, [α,β,α,α]=1, or (2) αρ=[α, β α], βρ=1, [α,β,β]=1. It is shown that for the solvability of the original embedding problem it is necessary and sufficient to have the solvability
of the associated Abelian and local problems for all completions of the base fields. Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 120–126.
Translated by V. V. Ishkhanov. 相似文献
18.
Yun-xia Li 《应用数学学报(英文版)》2006,22(4):615-626
In this paper we discuss the least-square estimator of the unknown change point in a mean shift for moving-average processes of ALNQD sequence. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained. The results are also true for ρ-mixing, φ-mixing, α-mixing sequences under suitable conditions. These results extend those of Bai, who studied the mean shift point of a linear process of i.i.d, variables, and the condition ∑j=0^∞j|aj| 〈 ∞ in Bai is weakened to ∑j=0^∞|aj|〈∞. 相似文献
19.
In this article, we consider a stationary α-mixing random field in IR
d. Under a large-sample scheme that is a mixture of the so-called “infill” and “increasing domain” asymptotics, we establish
a functional central limit theorem for the empirical processes of this random field. Further, we apply a blockwise bootstrap
to the samples. Under the condition that the side length of the block
for some 0 < β < 1, where λ
n
is the growth rate in the increasing domain asymptotics, we show that the bootstrapped empirical process converges weakly
to the same limiting Gaussian process almost surely. Extension to multivariate random fields and application to differentiable
statistical functionals are also given. A spatial version of the Bernstein’s inequality is developed, which may be of some
independent interest.
In final form 13 December 2004 相似文献
20.
Let τ be some triangulation of a planar polygonal domain Ω. Given a smooth functionu, we construct piecewise polynomial functionsv∈C
ρ(Ω) of degreen=3 ρ for ρ odd, andn=3ρ+1 for ρ even on a subtriangulation τ3 of τ. The latter is obtained by subdividing eachT∈ρ into three triangles, andv/T is a composite triangular finite element, generalizing the classicalC
1 cubic Hsieh-Clough-Tocher (HCT) triangular scheme. The functionv interpolates the derivatives ofu up to order ρ at the vertices of τ. Polynomial degrees obtained in this way are minimal in the family of interpolation schemes
based on finite elements of this type. 相似文献