共查询到20条相似文献,搜索用时 15 毫秒
1.
Wel Dong LIU Zheng Yan LIN 《数学学报(英文版)》2008,24(1):59-74
Let {X, X1, X2,...} be a strictly stationaryφ-mixing sequence which satisfies EX = 0,EX^2(log2{X})^2〈∞and φ(n)=O(1/log n)^Tfor some T〉2.Let Sn=∑k=1^nXk and an=O(√n/(log2n)^γ for some γ〉1/2.We prove that limε→√2√ε^2-2∑n=3^∞1/nP(|Sn|≥ε√ESn^2log2n+an)=√2.The results of Gut and Spataru (2000) are special cases of ours. 相似文献
2.
Let be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H,‖⋅‖) with covariance operator Σ, and set Sn=X1+?+Xn, n?1. Let . We prove that, for any 1<r<3/2 and a>−d/2,
3.
Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q(n)be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q(n)≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B(t)-inf0≤t≤sB(t),and B(t) is a Brownian bridge. 相似文献
4.
Let X, X1 , X2 , . . . be i.i.d. random variables, and set Sn = X1 +···+Xn , Mn = maxk≤n |Sk|, n ≥1. Let an = o( (n)(1/2)/logn). By using the strong approximation, we prove that, if EX = 0, VarX = σ2 0 and E|X| 2+ε ∞ for some ε 0, then for any r 1, lim ε1/(r-1)(1/2) [ε-2-(r-1)]∞∑n=1 nr-2 P{Mn ≤εσ (π2n/(8log n))(1/2) + an } = 4/π . We also show that the widest a n is o( n(1/2)/logn). 相似文献
5.
Let be a strictly stationary sequence of negatively associated random variables with zero mean and finite variance. We set and , . If , then for any , we show the precise rates of the first moment convergence in the law of the iterated logarithm for a kind of weighted infinite series of and as , and as . 相似文献
6.
Jiang Ye 《Journal of Mathematical Analysis and Applications》2007,327(1):695-714
Let be a sequence of i.i.d. random variables with EX=0 and EX2=σ2<∞. Set , Mn=maxk?n|Sk|, n?1. Let r>1, then we obtain
7.
J. Norkūunienė 《Lithuanian Mathematical Journal》2006,46(4):432-445
The strong convergence of dependent random variables is analyzed and the law of iterated logarithm for real additive functions
defined on the class
of combinatorial assemblies is obtained.
Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 532–547, October–December, 2006. 相似文献
8.
Karl Grill 《Journal of Theoretical Probability》1992,5(1):197-204
We investigate the upper limiting behavior of the distance of the normalize trajectories of a Wiener process from Strassen's class. It is shown that the right rate is (log logT)–2/3, improving previous results by the author and by Goodman and Kuelbs.(2,3) 相似文献
9.
J. Norkūnienė 《Lithuanian Mathematical Journal》2007,47(2):176-183
In [13], we investigated one-dimensional laws of iterated logarithm for additive functions defined on a class of combinatorial
assemblies. In this paper, we obtain a functional law of iterated logarithm.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 211–219, April–June, 2007. 相似文献
10.
Let {X, X n ; n?≥?1} be a sequence of i.i.d. random variables taking values in a real separable Hilbert space \((\textbf{H},\|\cdot\|)\) with covariance operator Σ. Set \(S_n=\sum_{i=1}^nX_i,\) n?≥?1. We prove that for 1?p?2 and r?>?1?+?p/2,where Y is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator Σ, and σ 2 is the largest eigenvalue of Σ.
相似文献
$\begin{array}{lll} &;\lim\limits_{\varepsilon\searrow0}\varepsilon^{(2r-p-2)/(2-p)}\sum\limits_{n=1}^\infty n^{r/p-2-1/p}{\mbox{\rm{\textsf{E}}}}\{\|S_n\|-\sigma\varepsilon n^{1/p}\}_+\\&;\quad\qquad\qquad\qquad=\sigma^{-(2r-2-p)/(2-p)}\frac{p(2-p)}{(r-p)(2r-p-2)}{\mbox{\rm{\textsf{E}}}}\|Y\|^{2(r-p)/(2-p)}, \end{array}$
11.
Hå kan Hedenmalm Ilgiz Kayumov 《Proceedings of the American Mathematical Society》2007,135(7):2235-2248
We obtain considerable improvement of Makarov's estimate of the boundary behavior of a general conformal mapping from the unit disk to a simply connected domain in the complex plane. We apply the result to improve Makarov's comparison of harmonic measure with Hausdorff measure on simply connected domains.
12.
Tian-xiao Pang Li-xin Zhang Jian-feng Wang 《Journal of Mathematical Analysis and Applications》2008,340(2):1249-1262
Let X,X1,X2,… be i.i.d. nondegenerate random variables with zero means, and . We investigate the precise asymptotics in the law of the iterated logarithm for self-normalized sums, Sn/Vn, also for the maximum of self-normalized sums, max1kn|Sk|/Vn, when X belongs to the domain of attraction of the normal law. 相似文献
13.
Yuexu Zhao 《Bulletin of the Brazilian Mathematical Society》2006,37(3):377-391
Let X1, X2, ... be i.i.d. random variables with EX1 = 0 and positive, finite variance σ2, and set Sn = X1 + ... + Xn. For any α > −1, β > −1/2 and for κn(ε) a function of ε and n such that κn(ε) log log n → λ as n ↑ ∞ and
, we prove that
*Supported by the Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. 20060237 and 20050494). 相似文献
14.
Miguel A. Arcones 《Journal of Theoretical Probability》1995,8(4):877-903
We present some optimal conditions for the compact law of the iterated logarithm of a sequence of jointly Gaussian processes
in different situations. We also discuss the local law of the iterated logarithm for Gaussian processes indexed by arbitrary
index sets, in particular for self-similar Gaussian processes. We apply these results to obtain the law of the iterated logarithm
for compositions of Gaussian processes.
Research partially supported by NSF Grant DMS-93-02583. 相似文献
15.
1. IntroductionLet {Xu, n 2 1} be a sequence of r.v.IS in the same probability space and put Sa =nZ Xi, n 2 1; L(x) = mad (1, logx).i=1Since the definition of complete convergence is illtroduced by Hsu and Robbins[6], therehave been many authors who devote themselves to the study of the complete convergence forsums of i.i.d. real-valued r.v.'s, and obtain a series of elegys results, see [3,7]. Meanwhile,the convergence rates in the law of logarithm of i.i.d. real-vained r.v.'s have also be… 相似文献
16.
17.
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
18.
Uwe Einmahl 《Probability Theory and Related Fields》1992,92(2):177-194
Summary In a previous paper we obtained upper and lower class type results refining the bounded LIL for sums of iid Hilbert space valued mean zero random variables, whose covariance operators satisfy certain regularity assumptions. We now establish precise convergence rates for the bounded LIL in the non-regular case. It turns out that the almost sure behavior in this case is entirely different from the behavior in the previous situation.Supported in part by NSF Grant DMS 90-05804 相似文献
19.
20.
假设{X_n,n≥1}为一列严平稳的NA随机变量,期望为零,方差有限.设S_n=∑_(i=1)~n∑X_i,M_n=max_(1≤i≤n)|S_i|.在适当的条件下,得到了一类NA序列部分和部分和最大值重对数矩收敛的精确渐近性. 相似文献