共查询到20条相似文献,搜索用时 125 毫秒
1.
Wei HUANG Ye JIANG Li Xin ZHANG 《数学学报(英文版)》2005,21(5):1057-1070
Let {X,Xn;n ≥ 1} be a strictly stationary sequence of ρ-mixing random variables with mean zeros and finite variances. Set Sn =∑k=1^n Xk, Mn=maxk≤n|Sk|,n≥1.Suppose limn→∞ESn^2/n=:σ^2〉0 and ∑n^∞=1 ρ^2/d(2^n)〈∞,where d=2 if 1≤r〈2 and d〉r if r≥2.We prove that if E|X|^r 〈∞,for 1≤p〈2 and r〉p,then limε→0ε^2(r-p)/2-p ∑∞n=1 n^r/p-2 P{Mn≥εn^1/p}=2p/r-p ∑∞k=1(-1)^k/(2k+1)^2(r-p)/(2-p)E|Z|^2(r-p)/2-p,where Z has a normal distribution with mean 0 and variance σ^2. 相似文献
2.
设环境q={q(n)}∞0是取值于[0,1]上一列独立同分布的随机变量列,且Eq(0)=p;{Sn}∞0是随机环境q中取整数值随机游动,S0=0,且满足:对任意的整数xi(i≥0),x,y,P(Sn+1=y|S1=x1,…,Sn-1=xn-1,Sn=x,q)={q(n),y=x+1,1-q(n),y=x-1,0,其他.我们证明了:p>1/2时,Sn→+∞,a.e.,n→∞;p<1/2时,Sn→-∞,a.e.,n→∞;p=1/2时,-∞=(lim infSn)/(n→+∞)<(lim supSn)/(n→+∞)=+∞,a.e.,n→∞. 相似文献
3.
4.
从 Newton运动学第二定律和 Newton万有引力定律出发 ,导出 Kepler行星绕日运动三定律 相似文献
5.
对一类有界独立或相依的随机变量序列|ξn|,获得了它的伯努利大数定律、波雷尔强大数定律及常返性定理.作为应用,得出了Loève专著[1]中的推广的伯努利大数定律、常返性定理,改进了[1]中的推广的波雷尔强大数定律. 相似文献
6.
7.
本文旨在给出概率论中的一个加强的强大数定律 ,并采用“子序列方法”予以证明 .一般地说 ,子序列方法旨在将一个子序列证明 (相对地说比较容易 )的结果扩张到整个序列上去 .定理 设 { Xn,n≥ 1 }为一随机变量序列 ,令Sn =∑nj=1Xj (1 ) 若诸 Xj不相关 ,且满足σ2 (Xn) =O(nθ) (θ≥ 0 ) (2 ) 则对任意满足α >3 2θ4(3 ) 的正数 α,有Sn -E(Sn)nα → 0 (n→∞ ) . a.e. (4) 证明 不失一般性 ,我们可以假设对每个 j,E(Xj) =0 ,则有E(S2n) =∑nj=1E(X2j) (5 ) 注意到 (2 )式有E(S2n)≤ O(n1 θ) . (6) … 相似文献
8.
李德立 《高校应用数学学报(A辑)》1990,(1)
设{X_n:n≥1}是在某可分Banach空间B上取值的独立随机变量序列,S_n=X_1+…+X_n,n≥1,对某0
0和>1,定义P_n(ε)=P(‖S_n‖/n~(1/p)≥ε)。本文的目的是研究当n→+∞时,P(ε)→0的速度,在Banach空间上推广了Heyde和Rohatgi的结果;同时,本文还讨论了P_n(ε)→0的速度与S_n/n~(1/p)→0 a.s.的关系问题。 相似文献
9.
关于《强大数定律成立的充要条件》一文的补正 总被引:1,自引:0,他引:1
In this note we point out a mistake of the article <The sufficient and necessary condition of SLLN>. 相似文献
10.
The authors achieve a general law of precise asymptotics for a new kind of complete moment convergence of i.i.d, random variables, which includes complete convergence as a special case. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in studies of complete convergence. This extends and generalizes the corresponding results of Liu and Lin in 2006. 相似文献
11.
Three results are obtained concerning the number of order preserving maps of an n-element partially ordered set to itself. We show that any such ordered set has at least 2
2n/3 order preserving maps (and 2
2
in the case of length one). Precise asymptotic estimates for the numbers of self-maps of crowns and fences are also obtained. In addition, lower bounds for many other infinite families are found and several precise problems are formulated.Supported by ONR Contract N00014-85-K-0769.Supported by NSF Grant DMS-9011850.Supported by NSERC Grants 69-3378 and 69-0259. 相似文献
12.
Maria Chudnovsky Gérard Cornuéjols Xinming Liu? Paul Seymour? Kristina Vu?kovi?? 《Combinatorica》2005,25(2):143-186
A graph is Berge if no induced subgraph of G is an odd cycle of length at least five or the complement of one. In this paper we give an algorithm to test if a graph G is Berge, with running time O(|V (G)|9). This is independent of the recent proof of the strong perfect graph conjecture.* Currently this author is a Clay Mathematics Institute Research Fellow.** Supported by NSF grant DMI-0352885 and ONR grant N00014-97-1-0196. Supported by ONR grant N00014-01-1-0608, and NSF grant DMS-0070912. Supported by EPSRC grant GR/R35629/01. 相似文献
13.
Paul Houston Ilaria Perugia Anna Schneebeli Dominik Schötzau 《Numerische Mathematik》2005,100(3):485-518
Summary In this paper, we introduce and analyze the interior penalty discontinuous Galerkin method for the numerical discretization of the indefinite time-harmonic Maxwell equations in the high-frequency regime. Based on suitable duality arguments, we derive a-priori error bounds in the energy norm and the L2-norm. In particular, the error in the energy norm is shown to converge with the optimal order (hmin{s,}) with respect to the mesh size h, the polynomial degree , and the regularity exponent s of the analytical solution. Under additional regularity assumptions, the L2-error is shown to converge with the optimal order (h+1). The theoretical results are confirmed in a series of numerical experiments.Supported by the EPSRC (Grant GR/R76615).Supported by the Swiss National Science Foundation under project 21-068126.02.Supported in part by the Natural Sciences and Engineering Council of Canada. 相似文献
14.
Shiri Artstein-Avidan Omer Friedland Vitali Milman Sasha Sodin 《Israel Journal of Mathematics》2006,156(1):141-155
We present a quantitative form of the result of Bai and Yin from [2], and use to show that the section of ℓ
1
(1+δ)n
spanned byn random independent sign vectors is with high probability isomorphic to euclidean with isomorphism constant polynomial in
δ−1.
Partially supported by BSF grant 2002-006.
Supported by the National Science Foundation under agreement No. DMS-0111298.
Supported in part by the Israel Science Academy. 相似文献
15.
If a Banach space has a LipschitzC
1-smooth bump function, then it admits other bumps of the same smoothness whose gradients exactly fill the dual unit ball and
other reasonable figures. This strengthens a result of Azagra and Deville who were able to cover the dual unit ball.
Supported in part by NSERC and the Canada Research Chair Programme.
Supported in part by grants NATO CRG-973982, GAĈR 201-01-1198, and AV 1019003 (Czech Republic).
Supported in part by NATO CRG-973982 and NSERC. 相似文献
16.
We consider several results, each of which uses some type of “L
2” estimate to provide information about harmonic measure on planar domains. The first gives an a.e. characterization of tangent
points of a curve in terms of a certain geometric square function. Our next result is anL
p
estimate relating the derivative of a conformal mapping to its Schwarzian derivative. One consequence of this is an estimate
on harmonic measure generalizing Lavrentiev’s estimate for rectifiable domains. Finally, we considerL
2 estimates for Schwarzian derivatives and the question of when a Riemann mapping ϕ has log ϕ′ in BMO.
Supported in part by NSF Grant DMS-91-00671.
Supported in part by NSF Grant DMS-86-025000. 相似文献
17.
We use a combination of both symbolic and numerical techniques to construct degree boundedC
k
-continuous, rational B-spline ε-approximations of real algebraic surface-surface intersection curves. The algebraic surfaces
could be either in implicit or rational parametric form. At singular points, we use the classical Newton power series factorizations
to determine the distinct branches of the space intersection curve. In addition to singular points, we obtain an adaptive
selection of regular points about which the curve approximation yields a small number of curve segments yet achievesC
k
continuity between segments. Details of the implementation of these algorithms and approximation error bounds are also provided.
Supported in part by NSF Grants CCR 92.22467, DMS 91-01424, AFOSR Grant F49620-10138 and NASA Grant NAG-1-1473.
Supported in part by K.C. Wong Education Foundation, Hong Kong. 相似文献
18.
We show that for each n ≥ 2 there is a quasi-isometric embedding of the hyperbolic space Hn in the product Tn=T × ··· × T of n copies of a (simplicial) metric tree T. On the other hand, we prove that there is no quasi-isometric embedding
for any metric tree T and any m ≥ 0.Mathematics Subject classification (2000). 54Exx.Supported by RFFI Grant 02-01-00090, CRDF Grant RMI-2381-ST-02 and SNF Grant 20-668 33.01. Supported by Swiss National Science Foundation. 相似文献
19.
Lutz Habermann 《Annals of Global Analysis and Geometry》1993,11(4):311-322
TheL
2-metric {ie311-1} on the moduli spaceM
1(Q) of self-dualSU(2)-connections with instanton number 1 over the Euclidean 4-space is described. It is shown that the Riemannian manifold (M
1(Q), {ie311-2}) is isometric to R+ × R4 with the Euclidean metric.Supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 288 相似文献
20.
Oleg Karpenkov 《Functional Analysis and Other Mathematics》2006,1(1):17-35
We completely describe lattice convex polytopes in ℝ
n
(for any dimension n) that are regular with respect to the group of affine transformations preserving the lattice.
Supported in part by the RFBR (Grant Nos. SS-1972.2003.1 and 05-01-01012a) and the NWO-RFBR (Grant No. 047.011.2004.026/RFBR
No. 05-02-89000-NWO_a). 相似文献