共查询到20条相似文献,搜索用时 640 毫秒
1.
Vladislav Kargin 《Probability Theory and Related Fields》2007,139(3-4):397-413
Let X
i
denote free identically-distributed random variables. This paper investigates how the norm of products behaves as n approaches infinity. In addition, for positive X
i
it studies the asymptotic behavior of the norm of where denotes the symmetric product of two positive operators: . It is proved that if EX
i
= 1, then is between and c
2
n for certain constant c
1 and c
2. For it is proved that the limit of exists and equals Finally, if π is a cyclic representation of the algebra generated by X
i
, and if ξ is a cyclic vector, then for all n. These results are significantly different from analogous results for commuting random variables. 相似文献
2.
We study the irrational factor function I(n) introduced by Atanassov and defined by , where is the prime factorization of n. We show that the sequence {G(n)/n}
n≧1, where G(n) = Π
ν=1
n
I(ν)1/n
, is convergent; this answers a question of Panaitopol. We also establish asymptotic formulas for averages of the function
I(n).
Research of the third author is supported in part by NSF grant number DMS-0456615. 相似文献
3.
Zheng Yan LIN Sung Chul LEE 《数学学报(英文版)》2006,22(2):535-544
Let {Xn,n ≥ 0} be an AR(1) process. Let Q(n) be the rescaled range statistic, or the R/S statistic for {Xn} which is given by (max1≤k≤n(∑j=1^k(Xj - ^-Xn)) - min 1≤k≤n(∑j=1^k( Xj - ^Xn ))) /(n ^-1∑j=1^n(Xj -^-Xn)^2)^1/2 where ^-Xn = n^-1 ∑j=1^nXj. In this paper we show a law of iterated logarithm for rescaled range statistics Q(n) for AR(1) model. 相似文献
4.
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
5.
Li Xin Zhang 《数学学报(英文版)》2008,24(4):631-646
Let X, X1, X2,... be i.i.d, random variables with mean zero and positive, finite variance σ^2, and set Sn = X1 +... + Xn, n≥1. The author proves that, if EX^2I{|X|≥t} = 0((log log t)^-1) as t→∞, then for any a〉-1 and b〉 -1,lim ε↑1/√1+a(1/√1+a-ε)b+1 ∑n=1^∞(logn)^a(loglogn)^b/nP{max κ≤n|Sκ|≤√σ^2π^2n/8loglogn(ε+an)}=4/π(1/2(1+a)^3/2)^b+1 Г(b+1),whenever an = o(1/log log n). The author obtains the sufficient and necessary conditions for this kind of results to hold. 相似文献
6.
Djellout Hacène Guillin Arnaud Wu Liming 《Statistical Inference for Stochastic Processes》1999,2(3):195-225
For a diffusion process dXt = σdB
t + b(t, Xt)dt with (σ
t
) unknown, we study the large and moderate deviations of the estimator
of the quadratic variational process
.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
7.
Precise Rates in the Law of Iterated Logarithm for the Moment of I.I.D. Random Variables 总被引:1,自引:0,他引:1
Ye JIANG Li Xin ZHANG 《数学学报(英文版)》2006,22(3):781-792
Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1+X2+…+Xn,Mn=max k≤n│Sk│,n≥1.Let an=O(1/loglogn).In this paper,we prove that,for b〉-1,lim ε→0 →^2(b+1)∑n=1^∞ (loglogn)^b/nlogn n^1/2 E{Mn-σ(ε+an)√2nloglogn}+σ2^-b/(b+1)(2b+3)E│N│^2b+3∑k=0^∞ (-1)k/(2k+1)^2b+3 holds if and only if EX=0 and EX^2=σ^2〈∞. 相似文献
8.
Jörg Eschmeier 《Archiv der Mathematik》2009,92(5):461-475
We use a variant of Grothendieck’s comparison theorem to show that, for a Fredholm tuple T ∈ L(X)n on a complex Banach space, there are isomorphisms . We conclude that a Fredholm tuple T ∈ L(X)n satisfies Bishop’s property (β) at z = 0 if and only if the vanishing conditions hold for . We apply these observations and results from commutative algebra to show that a graded tuple on a Hilbert space is Fredholm if and only if it satisfies Bishop’s property (β) at z = 0 and that, in this case, its cohomology groups can grow at most like kp.
Received: 14 January 2009 相似文献
9.
In this paper we prove that any residue class λ modulo a large prime number p can be represented in the form
for some positive integers m1, n1,... ,m5, n5 of the size O(p27/28). This improves one of the results from [6] on representability of λ modulo p in the form
with
. We also prove that any residue class modulo p can be represented in the form
with
. This improves the result of [7].
Received: 27 March 2006 相似文献
10.
Summary. Let k ≥ 1 be any integer. Let G be a finite abelian group of exponent n. Let sk(G) be the smallest positive integer t such that every sequence S in G of length at least t has a zero-sum subsequence of length kn. We study this constant for groups
when d = 3 or 4. In particular, we prove, as a main result, that
for every k ≥ 4,
and
for every prime p ≥ 5. 相似文献
11.
In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts. For each a>0, let $\{Y^{(a)}_{n}:n\ge1\}In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts.
For each a>0, let {Y(a)n:n 3 1}\{Y^{(a)}_{n}:n\ge1\} be a sequence of independent and identically distributed random variables and {X(a)t:t 3 0}\{X^{(a)}_{t}:t\ge0\} be a Lévy process such that X1(a)=dY1(a)X_{1}^{(a)}\stackrel{d}{=}Y_{1}^{(a)},
\mathbbEX1(a) < 0\mathbb{E}X_{1}^{(a)}<0 and
\mathbbEX1(a)-0\mathbb{E}X_{1}^{(a)}\uparrow0 as a↓0. Let S(a)n=?k=1n Y(a)kS^{(a)}_{n}=\sum _{k=1}^{n} Y^{(a)}_{k}. Then, under some mild assumptions, , for some random variable and some function Δ(⋅). We utilize this result to present a number of limit theorems for suprema of Lévy processes in the
heavy-traffic regime. 相似文献
12.
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
13.
We investigate the joint weak convergence (f.d.d. and functional) of the vector-valued process (U
n
(1)
(τ), U
n
(2)
(τ)) for τ ∈ [0, 1], where
and
are normalized partial-sum processes separated by a large lag m, m/n → ∞, and (X
t
, t ∈ ℤ) is a stationary moving-average process with i.i.d. (or martingale-difference) innovations having finite variance. We
consider the cases where (X
t
) is a process with long memory, short memory, or negative memory. We show that, in all these cases, as n → ∞ and m/n → ∞, the bivariate partial-sum process (U
n
(1)
(τ), U
n
(2)
(τ)) tends to a bivariate fractional Brownian motion with independent components. The result is applied to prove the consistency
of certain increment-type statistics in moving-average observations.
This work supported by the joint Lithuania-French research program Gilibert.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 479–500, October–December, 2005. 相似文献
14.
Define
, where
is a symmetric U-type statistic, H
k() is the Hermite polynomial of degree k, and {X, X
n, n1} are independent identically distributed binary random variables with Pr(X{–1, 1}})=1. We show that
according as EX=0 or EX0, respectively. 相似文献
15.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
16.
Xiugui Liu 《Archiv der Mathematik》2008,90(5):471-480
Let X = {x
1, …, x
n
} be a set of n points in the d-dimensional Euclidean space , with unit diameter. In this work we give the complete proof of a conjecture by Witsenhausen, stating that the maximum M(d, n) of in dimension d is attained if and only if the points are distributed as evenly as possible among the vertices of a regular d-dimensional simplex of edge-length 1.
Received: 5 July 2007, Revised: 22 October 2007 相似文献
17.
L. V. Rozovsky 《Journal of Mathematical Sciences》2009,159(3):341-349
Let Sn = X1 + · · · + X
n
, n ≥ 1, and S
0 = 0, where X
1, X
2, . . . are independent, identically distributed random variables such that the distribution of S
n/B
n converges weakly to a nondeoenerate distribution F
α
as n → ∞ for some positive B
n
. We study asymptotic behavior of sums of the form
where
a function d(t) is continuous at [0,1] and has power decay at zero,
Bibliography: 13 titles.
Translated from Zapiski Nauchnylch Serninarov POMI, Vol. 361, 2008, pp. 109–122. 相似文献
18.
Jugal Ghorai 《Annals of the Institute of Statistical Mathematics》1980,32(1):341-350
LetX
1,...,X
n
be i.i.d. random variable with a common densityf. Let
be an estimate off(x) based on a complete orthonormal basis {φ
k
:k≧0} ofL
2[a, b]. A Martingale central limit theorem is used to show that
, where
and
. 相似文献
19.
A Gaussian t-design is defined as a finite set X in the Euclidean space ℝn satisfying the condition:
for any polynomial f(x) in n variables of degree at most t, here α is a constant real number and ω is a positive weight function on X. It is easy to see that if X is a Gaussian 2e-design in ℝn, then
. We call X a tight Gaussian 2e-design in ℝn if
holds. In this paper we study tight Gaussian 2e-designs in ℝn. In particular, we classify tight Gaussian 4-designs in ℝn with constant weight
or with weight
. Moreover we classify tight Gaussian 4-designs in ℝn on 2 concentric spheres (with arbitrary weight functions). 相似文献
20.
Fazli Kh 《Statistical Inference for Stochastic Processes》2007,10(2):181-208
We observe a realization X
(n) of a Poisson process on the set
with intensity function
depending on the unknown real parameter
. Based on X
(n) we test simple null hypothesis
against one sided alternative
for given
. We improve the level of the well-known locally asymptotically uniformly most powerful (LAUMP) test by using the Edgeworth
type expansion for stochastic integral. We show that the improved test is second-order efficient under certain regularity
conditions.
相似文献