共查询到18条相似文献,搜索用时 230 毫秒
1.
对相协随机变量部分和建立一些指数不等式, 这些不等式改进了Ioannides和Roussas (1999)及Oliveira (2005) 所获得的相应结论.利用这些不等式给出一些强大数律, 对协方差系数为几何递减情形,获得了强大数律的收敛速度为n-1/2(log log n)1/2(log n).这个收敛速度接近独立随机变量的重对数律的速度, 而且较好地改进Ioannides 和 Roussas及Oliveira分别获得的速度n-1/3}(log n)2/3和n-1/3(log n)5/3. 相似文献
2.
设{Xn, n ≥1}是独立同分布随机变量序列, Un 是以对称函数(x, y) 为核函数的U -统计量. 记Un =2/n(n-1)∑1≤i h(Xi, Xj), h1(x) =Eh(x, X2). 在一定条件下, 建立了∑n=2∞(logn)δ-1EUn2I {I U n |≥n 1/2√lognε}及∑n=3∞(loglognε)δ-1/logn EUn2 I {|U n|≥n1/2√log lognε} 的精确收敛速度. 相似文献
3.
4.
设Pn(x)为[0,∞)上次数不超过n的代数多项式,则有‖p′n(x)e-x‖[0,∞)≤(6.3n+1)‖pn(x)e-x‖[0,∞).若pn(x)同时又是奇函数或偶函数,则有‖p′n(x)e-x‖[0,∞)≤(1.8+7n1/2)‖p相似文献
5.
切于已知球的单形宽度 总被引:3,自引:1,他引:2
Let w(△n) denote the width of a non-degenerate simplex △n in En and r(△n) denote the inradius of the simplex.Then, in this paper, we prove the ine-qunlity as below: Theorem:w(△n)≤βnr(△n) where βn =(n1/2(n+1))/([(n+1)/2]1/2(n+1-[(n+1)/2])1/2) The equality holds if and only if the simplex is regular. 相似文献
6.
设{X,Xn;n≥1}是在可分Banach空间(B,‖·‖)中取值的独立同分布随机变量序列,并且EX=0,Ef2(X)<+∞,f∈B*,记Sn=X1+…+Xn,n≥1.本文的目的是在适当的充要条件下研究和的收敛速度.作为本文结果的应用,分别给出了X满足有界叠对数律和紧叠对数律各一个新的充要条件;同时,本文改进了文献[3]和[4]在实空间情形所建立的一些结果. 相似文献
7.
8.
金敬森 《数学物理学报(A辑)》2009,29(4):1138-1143
设d是一个正整数, N d是d -维正整数格点.设{Xn , n∈N d} 是一同分布的负相伴随机场, 记Sn =∑k≤ n Xk, Sn(k)=Sn-Xk, 如果r >2, EX1 = 0 和σ2= Var(X1}, 则存在一个正数M:=100√(r-2)(1+σ2)使得下列条件等价
(I)E |X1|r (log|X1|)d-1-r/2 <∞;
(II)∑n∈ Nd |n|r/2-2P(max1≤ k≤ n |Sn(k)|≥ (2d+1 )ε√|n| log |n |) <∞,∨ε > M;
(III)∑n∈N d |n|r/2-2P(max1≤ k≤n |Sk |≥ε√| n} log| n |) <∞,∨ε > M.
(III)\ \ $\sum\limits_{{{\bf n}}\in {{\cal N}}^{d}} |n|^{r/2-2}
P(\max\limits_{{\bf 1}\leq{\bf k}\leq{\bf n}}|S_{{\bf k}}|\geq
\varepsilon \sqrt{|{\bf n}|\log |{\bf n}|})<\infty$,
$\forall\varepsilon>M$. 相似文献
9.
Let f(x)∈C[-1,1],Tn(x)=cos (n arccos x),Un(x)=(sin((n+1)arccosx))/(1-x2)1/2,Pn(x) be the Legendre polynomials of degree n. And let ω(t ) be a given modulus of continuity, Hω={f|ω(f,t)≤ω(t)}.A. K. Sharma and J. Tzimbalario(J. Appro. Th., 13(1975), 431-442) considered the operators Ln,p (f, x) (p= 0, 1, 2,3) and obtained some theorems.In this paper, we prove the following theorems. 相似文献
10.
右半平面内解析函数的准确零(R)级 总被引:6,自引:2,他引:4
Let f(s)=(?)ane-λm3(s=σ+it),0<λn↑+∞), where (?)(n/logU(λn))=E<+∞,(?)(log|αn|/λn)=0. 相似文献
11.
Exponential Inequalities and Complete Convergence for Extended Negatively Dependent Random Variables
SHEN Ai-ting ZHU Hua-yan ZHANG Ying 《数学季刊》2014,(3):344-355
Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequality for negative dependent sequence. Communications of the Korean Mathematical Society, 2007, 22(2): 315-321) and Nooghabi and Azarnoosh(Exponential inequality for negatively associated random variables. Statisti- cal Papers, 2009, 50 (2): 419-428). We also obtain the convergence rate O(n-1/2 In1/2 n) for the strong law of large numbers, which improves the corresponding ones of Kim and Kim, and Nooghabi and Azarnoosh. 相似文献
12.
Shan-chao YANG & Min CHEN Deptartment of Mathematics Guangxi Normal University Guilin China Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2007,50(5):705-714
Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(logn) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3(logn)2/3 and n-1/3(logn)5/3, separately. 相似文献
13.
We present some exponential inequalities for positively associated unbounded random variables. By these inequalities, we obtain
the rate of convergence n
−1/2
β
n
log 3/2
n in which β
n
can be particularly taken as (log log n)1/σ
with any σ>2 for the case of geometrically decreasing covariances, which is faster than the corresponding one n
−1/2(log log n)1/2log 2
n obtained by Xing, Yang, and Liu in J. Inequal. Appl., doi: (2008) for the case mentioned above, and derive the convergence rate n
−1/2
β
n
log 1/2
n for the above β
n
under the given covariance function, which improves the relevant one n
−1/2(log log n)1/2log n obtained by Yang and Chen in Sci. China, Ser. A 49(1), 78–85 (2006) for associated uniformly bounded random variables. In addition, some moment inequalities are given to prove the main results,
which extend and improve some known results. 相似文献
14.
D. W. Matula 《Combinatorica》1987,7(3):275-284
The expose-and-merge paradigm for exploring random graphs is presented. An algorithm of complexityn O(logn) is described and used to show that the chromatic number of a random graph for any edge probability 0<p<1 falls in the interval $$\left[ {\left( {\frac{1}{2} - \varepsilon } \right)\log (1/(1 - p))\frac{n}{{\log n}}, \left( {\frac{2}{3} + \varepsilon } \right)\log (1/(1 - p))\frac{n}{{\log n}}} \right]$$ with probability approaching unity asn→∞. 相似文献
15.
Zheng Zukang 《数学学报(英文版)》1994,10(4):337-347
LetX
1,X
2, ...,X
n
be a sequence of nonnegative independent random variables with a common continuous distribution functionF. LetY
1,Y
2, ...,Y
n
be another sequence of nonnegative independent random variables with a common continuous distribution functionG, also independent of {X
i
}. We can only observeZ
i
=min(X
i
,Y
i
), and
. LetH=1−(1−F)(1−G) be the distribution function ofZ. In this paper, the limit theorems for the ratio of the Kaplan-Meier estimator
or the Altshuler estimator
to the true survival functionS(t) are given. It is shown that (1)P(δ(n)=1 i.o.)=0 ifF(τ
H
) < 1 andP(δ
n
=0 i.o. )=0 ifG(τH) > 1 where δ(n) is the corresponding indicator function of
and
have the same order
a.s., where {T
n
} is a sequence of constants such that 1−H(T
n
)=n
−α(logn)β(log logn)γ. 相似文献
16.
Friedrich Roesler 《Archiv der Mathematik》1999,73(3):193-198
Abstract. For natural numbers n we inspect all factorizations n = ab of n with a £ ba \le b in \Bbb N\Bbb N and denote by n=an bnn=a_n b_n the most quadratic one, i.e. such that bn - anb_n - a_n is minimal. Then the quotient k(n) : = an/bn\kappa (n) := a_n/b_n is a measure for the quadraticity of n. The best general estimate for k(n)\kappa (n) is of course very poor: 1/n £ k(n) £ 11/n \le \kappa (n)\le 1. But a Theorem of Hall and Tenenbaum [1, p. 29], implies(logn)-d-e £ k(n) £ (logn)-d(\log n)^{-\delta -\varepsilon } \le \kappa (n) \le (\log n)^{-\delta } on average, with d = 1 - (1+log2 2)/log2=0,08607 ?\delta = 1 - (1+\log _2 \,2)/\log 2=0,08607 \ldots and for every e > 0\varepsilon >0. Hence the natural numbers are fairly quadratic.¶k(n)\kappa (n) characterizes a specific optimal factorization of n. A quadraticity measure, which is more global with respect to the prime factorization of n, is k*(n): = ?1 £ a £ b, ab=n a/b\kappa ^*(n):= \textstyle\sum\limits \limits _{1\le a \le b, ab=n} a/b. We show k*(n) ~ \frac 12\kappa ^*(n) \sim \frac {1}{2} on average, and k*(n)=W(2\frac 12(1-e) log n/log 2n)\kappa ^*(n)=\Omega (2^{\frac {1}{2}(1-\varepsilon ) {\log}\, n/{\log} _2n})for every e > 0\varepsilon>0. 相似文献
17.
Let n = (p − 1) · p
k
, where p is a prime number such that 2 is a primitive root modulo p, and 2
p−1 − 1 is not a multiple of p
2. For a standard basis of the field GF(2
n
), a multiplier of complexity O(log log p)n log n log log
p
n and an inverter of complexity O(log p log log p)n log n log log
p
n are constructed. In particular, in the case p = 3 the upper bound
$
5\frac{5}
{8}n\log _3 n\log _2 \log _3 n + O(n\log n)
$
5\frac{5}
{8}n\log _3 n\log _2 \log _3 n + O(n\log n)
相似文献
18.
Jun Wu 《Monatshefte für Mathematik》2008,19(1):83-87
For an irrational number x and n ≥ 1, we denote by k
n
(x) the exact number of partial quotients in the continued fraction expansion of x given by the first n decimals of x. G. Lochs proved that for almost all x, with respect to the Lebesgue measure
In this paper, we prove that an iterated logarithm law for {k
n
(x): n ≥ 1}, more precisely, for almost all x,
for some constant σ > 0.
Author’s address: Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. China 相似文献
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