共查询到20条相似文献,搜索用时 15 毫秒
1.
Let be a sequence of real-valued i.i.d. random variables with E(X)=0 and E(X2)=1, and set , n?1. This paper studies the precise asymptotics in the law of the iterated logarithm. For example, using a result on convergence rates for probabilities of moderate deviations for obtained by Li et al. [Internat. J. Math. Math. Sci. 15 (1992) 481-497], we prove that, for every b∈(−1/2,1],
2.
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
3.
Dianliang Deng 《Journal of Mathematical Analysis and Applications》2011,376(1):136-153
Let X,X1,X2,… be a sequence of nondegenerate i.i.d. random variables with zero means. Set Sn=X1+?+Xn and . In the present paper we examine the precise asymptotic behavior for the general deviation probabilities of self-normalized sums, Sn/Wn. For positive functions g(x), ?(x), α(x) and κ(x), we obtain the precise asymptotics for the following deviation probabilities of self-normalized sums:
4.
Jiang Chaowei Yang Xiaorong 《高校应用数学学报(英文版)》2007,22(1):87-94
In the case of Zd (d ≥ 2)-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k ∈ Zd } i.i.d. random variables with mean 0, Sn = ∑k≤nXk and Vn2 = ∑j≤nX2j, the precise asymptotics for ∑n1/|n|(log|n|)dP(|Sn/vn|≥ ε√loglog|n|) and ∑n(logn|)δ/|n|(log|n|)d-1 P(|Sn/Vn| ≥ ε√log n), as ε ↘ 0, is established. 相似文献
5.
设X,X_1,X_2,…为零均值、非退化、吸引域为正态吸引场的独立同分布随机变量序列,记S_n=■X_j,M_n=■|S_k|,V_n~2=■X_j~2,n≥1.证明了当b>-1时,■δ~(-2(b 1))■(log log n)~P/(n log n)P(Mn/V_n≤ε~(π~2)/(8lgo log n)~(1/2)) =4/πГ(b 1)■~(-1)~k/(2k 1)~(2b 3). 相似文献
6.
Terence Chan 《Journal of Theoretical Probability》1995,8(3):643-667
For 0<<1, let
. The questions addressed in this paper are motivated by a result due to Strassen: almost surely, lim sup
t
U
((t))=1–exp{–4(–1)–1}. We show that Strassen's result is closely related to a large deviations principle for the family of random variablesU
(t), t>0. Also, when =1,U
(t)0 almost surely and we obtain some bounds on the rate of convergence. Finally, we prove an analogous limit theorem for discounted averages of the form
as 0, whereD is a suitable discount function. These results also hold for symmetric random walks. 相似文献
7.
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
8.
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.
9.
A self-normalized law of the iterated logarithm for the geometrically weighted random series 下载免费PDF全文
Let {X, X_n; n ≥ 0} be a sequence of independent and identically distributed random variables with EX=0, and assume that EX~2I(|X| ≤ x) is slowly varying as x →∞, i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series Σ~∞_(n=0)β~nX_n(0 β 1) is obtained, under some minimal conditions. 相似文献
10.
T. E. Duncan 《Journal of multivariate analysis》1975,5(4):425-433
Some function space laws of the iterated logarithm for Brownian motion with values in finite and infinite dimensional vector spaces are shown to follow from Hincin's classical law of the iterated logarithm and some martingale techniques. A law of the iterated logarithm for Brownian motion in a differentible manifold is also stated. 相似文献
11.
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
12.
An open queueing network model in heavy traffic is developed. Such models are mathematical models of computer networks in heavy traffic. Laws of the iterated logarithm for the virtual waiting time of the customer in open queueing networks and homogeneous computer networks are proved. 相似文献
13.
H.S.F Wong 《Journal of multivariate analysis》1981,11(3):346-353
An analogue of the law of the iterated logarithm for Brownian motion in Banach spaces is proved where the expression √2 loglog s is replaced by a positive non-decreasing function satisfying certain conditions. 相似文献
14.
The Levy's type maximal inequality is a key to establish the law of the iterated logarithm for associated random variables. Unfortunately, this type inequality cannot be obtained for a generalization of association, i.e., linear positive quadrant dependence, because of their special dependence structure. The purpose of this paper is to provide a different approach to obtain a law of the iterated logarithm for a sequence of linear positive quadrant dependent random variables. 相似文献
15.
We establish the law of the iterated logarithm for the product limit estimator, when the data are subject to double censoring. This investigation extends the results available for the model for singly censored data. 相似文献
16.
The recent interest in iterated Wiener processes was motivated by apparently quite unrelated studies in probability theory and mathematical statistics. Laws of the iterated logarithm (LIL) were independently obtained by Burdzy(2) and Révész(17). In this work, we present a functional version of LIL for a standard iterated Wiener process, in the spirit of functional asymptotic results of an 2-valued Gaussian process given by Deheuvels and Mason(9) in view of Bahadur-Kiefer-type theorems. Chung's liminf sup LIL is established as well, thus providing further insight into the asymptotic behavior of iterated Wiener processes. 相似文献
17.
汪嘉冈 《应用数学学报(英文版)》1994,10(1):59-68
ALAWOFTHEITERATEDLOGARITHMFORPROCESSESWITHINDEPENDENTINCREMENTSWANGJIAGANG(汪嘉冈)(EastChinaUniversityofScience&Technology,Shang... 相似文献
18.
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
19.
Hwai-Chung Ho 《Journal of Theoretical Probability》1995,8(2):347-360
It is shown in the present paper that the upper-half law of the iterated logarithm with the usual norming rate
still holds for certain class of non-instantaneous filters of strongly dependent Gaussian sequences. 相似文献
20.
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