共查询到20条相似文献,搜索用时 15 毫秒
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NA序列重对数律的几个极限定理 总被引:5,自引:2,他引:5
设{X_n;n≥1}均值为零、方差有限的NA平稳序列。记S_n=∑_(k=1)~n X_k,M_n=maxk≤n|S_k|,n≥1.假设σ~2=EX_1~2+2∑_(k=2)~∞EX_1X_k>0。本文讨论了:当ε 0时,P{M_n≥εσ(2nloglogn)~(1/2)的一类加权级数的精确渐近性质,以及当ε∞时,P{M_n≤εσ(π~2n/(8loglogn))~(1/2)}的一类加权级数的精确渐近性质。这些性质与重对数律和Chung重对数律的速度有关。 相似文献
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迭代Brown运动的一个Chung型重对数律 总被引:1,自引:0,他引:1
X及Y分别为Rd1及Rd2中的相互独立的标准Brown运动,满足X(0)=Y(0)=0.定义,称为一个迭代Brown运动.本文给出了关于Zd1,d2的一个Chung型重对数律. 相似文献
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Let
be a real separable Banach space and {X, X
n, m; (n, m) N
2} B-valued i.i.d. random variables. Set
. In this paper, the compact law of the iterated logarithm, CLIL(D), for B-valued random variables with two-dimensional indices ranging over a subset D of N
2 is studied. There is a gap between the moment conditions for CLIL(N
1) and those for CLIL(N
2). The main result of this paper fills this gap by presenting necessary and sufficient conditions for the sequence
to be almost surely conditionally compact in B, where, for 0, 1 r 2, N
r
(, ) = {(n, m) N
2; n
m n
exp{(log n)
r–1 (n)}} and (·) is any positive, continuous, nondecreasing function such that (t)/(log log t) is eventually decreasing as t , for some > 0. 相似文献
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证明了关于独立同分布随机变量序列的加权U-统计量的一个重对数律,类似于献「3」证明了一个加权U-统计量的解耦不等式。 相似文献
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Fu Qing Gao 《数学学报(英文版)》2009,25(2):209-222
Three types of laws of the iterated logarithm (LIL) for locally square integrable martingales with continuous parameter are considered by a discretization approach. By this approach, a lower bound of LIL and a number of FLIL are obtained, and Chung LIL is extended. 相似文献
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Laws of the iterated logarithm are established for the local U-statistic process. This entails the development of probability
inequalities and moment bounds for U-processes that should be of separate interest. The local U-statistic process is based
upon an estimator of the density of a function of several i.i.d. variables proposed by Frees (J. Am. Stat. Assoc. 89, 517–525, 1994). As a consequence, our results are directly applicable to the derivation of exact rates of uniform in bandwidth consistency
in the sup and in the L
p
norms for these estimators.
Research of E. Giné partially supported by NSA Grant H98230-04-1-0075.
Research of D.M. Mason partially supported by NSA Grant MDA904-02-1-0034 and NSF Grant DMS-0503908. 相似文献
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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
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设{xn,m≥1}是独立同分布随机变量序列,EX1=0,EX12=1.设Tn= Tn(X1,…,Xn)是随机函数且Tn=Sn Rn.本文证明在E|Rn|2∨r<∞或E|Rn|<∞下,对随机函数Tn成立着Baum-Katz强大数律和重对数律的精确极限性质的一般结果.由此作为推论,对U-统计量,Von-Mises统计量,线性过程,移动平均过程,线性模型中误差方差估计和功率和等在适当矩条件下均可写出Baum-Katz强大数律和重对数律的精确极限性质. 相似文献
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The usual law of the iterated logarithm states that the partial sums Sn of independent and identically distributed random variables can be normalized by the sequence an = √nlog log n, such that limsupn→∞ Sn/an = √2 a.s. As has been pointed out by Gut (1986) the law fails if one considers the limsup along subsequences which increase faster than exponentially. In particular, for very rapidly increasing subsequences {nk≥1} one has limsupk→∞ Snk/ank = 0 a.s. In these cases the normalizing constants ank have to be replaced by √nk log k to obtain a non-trivial limiting behaviour: limsupk→∞ Snk/ √nk log k = √2 a.s. We will present an intelligible argument for this structural change and apply it to related results. 相似文献
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本文借助于Hoelder范数在函数空间中诱导出的强拓扑下的大偏差公式,得到了Wiener过程在Hoelder范数下的泛函重对数定律. 相似文献
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《随机分析与应用》2013,31(1):181-203
Abstract We consider a sequence (Z n ) n≥1 defined by a general multivariate stochastic approximation algorithm and assume that (Z n ) converges to a solution z* almost surely. We establish the compact law of the iterated logarithm for Z n by proving that, with probability one, the limit set of the sequence (Z n ? z*) suitably normalized is an ellipsoid. We also give the law of the iterated logarithm for the l p norms, p ∈ [1, ∞], of (Z n ? z*). 相似文献
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对于多指标独立同分布的随机变量序列,在某些更广泛的正则化序列下,本文给出了重对数律成立的充分必要条件.作为应用,本文讨论了正则和极大值函数的矩存在的充分必要条件. 相似文献
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在该文中,作者应用扩散过程在Holder范数下的大偏差得到了扩散过程在Holder范数下的局部Strassen重对数律. 并且还得到了重Ito积分的泛函重对数律. 相似文献