共查询到20条相似文献,搜索用时 15 毫秒
1.
LuCHUANRONG 《高校应用数学学报(英文版)》1997,12(4):375-380
Let(x1,j≥1)be a sequence of negatively associated random variables with ex1=o,ex^21<∞.in this paper a functional central limit theorem for negatively associated random variables under some conditions withbout stationarity is proved which is the same as the results for positively associated random variables. 相似文献
2.
We construct an independent increments Gaussian process associated to a class of multicolor urn models. The construction uses
random variables from the urn model which are different from the random variables for which central limit theorems are available
in the two color case. 相似文献
3.
Let X1, …, Xn be independent random variables and define for each finite subset I {1, …, n} the σ-algebra
= σ{Xi : i ε I}. In this paper
-measurable random variables WI are considered, subject to the centering condition E(WI
) = 0 a.s. unless I J. A central limit theorem is proven for d-homogeneous sums W(n) = ΣI = dWI, with var W(n) = 1, where the summation extends over all (nd) subsets I {1, …, n} of size I = d, under the condition that the normed fourth moment of W(n) tends to 3. Under some extra conditions the condition is also necessary. 相似文献
4.
Brice Franke 《Probability Theory and Related Fields》2005,133(2):236-244
We prove a functional central limit theorem for diffusions on periodic sub- manifolds of ℝN. The proof is an adaptation of a method presented in [BenLioPap] and [Bha] for proving functional central limit theorems for diffusions with periodic drift vectorfields. We then apply the central limit theorem in order to obtain a recurrence and a transience criterion for periodic diffusions. Other fields of applications could be heat-kernel estimates, similar to the ones obtained in [Lot].Mathematics Subject Classification (2000): 35B27, 60F05, 58J65The author wants to express his gratitude toward the National Cheng Kung University in Tainan (Taiwan) for its kind hospitality. 相似文献
5.
Continuing an earlier work [4], properties of canonical Wiener processes are investigated. An analog of the sample path continuity property is obtained. A noncommutative counterpart of weak convergence is formulated. Operator processes (Pn, Qn) analogous to the random-walk approximating processes of the Donsker invariance principle are defined in terms of a sequence (pi, qi) of pairs of quantum mechanical canonical observables satisfying hypotheses analogous to those of the classical central limit theorem. It is shown that Pn, Qn) converges weakly to a canonical Wiener process. 相似文献
6.
The functional central limit theorem for linear processes with strong near-epoch dependent innovations 总被引:1,自引:0,他引:1
This paper discusses linear processes with innovations exhibiting asymptotic weak dependence by being strong near-epoch dependent functions of mixing processes. The functional central limit theorem for the normalized partial sum process is established. The conditions given essentially improve on existing results in the literature in terms of the “size” requirement for the amount of dependence. It is also shown that two important econometric models, ARMA and GARCH models, are strong near-epoch dependent sequences. 相似文献
7.
Central limit theorem and almost sure central limit theorem for the product of some partial sums 总被引:1,自引:0,他引:1
Miao Yu 《Proceedings Mathematical Sciences》2008,118(2):289-294
In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of
independent identically distributed random variables. 相似文献
8.
We study the problem of convergence in distribution of a suitably normalized sum of stationary associated random variables.
We focus on the infinite variance case. New results are announced.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
Nguyen Tien Dung 《随机分析与应用》2019,37(1):74-89
In this paper, we consider a general class of functionals of stochastic differential equations driven by fractional Brownian motion. For this class, we obtain Gaussian estimates for the density and a quantitative central limit theorem. The main tools of the paper are the techniques of Malliavin calculus. 相似文献
10.
Anscombe (1952) (also see Chung (1974)) has developed a central limit theoremof random sums of independent and identically distributed random variables. Applicability of this theorem in practice, however, is limited since the normalization requires random factors. In this paper we establish sufficient conditions under which the central limit theorem holds when such random factors are replaced by the underlying asymptotic mean and standard ddeviation. An application of this result in the context of shock models is also given. 相似文献
11.
Katusi Fukuyama Shigeru Takahashi 《Proceedings of the American Mathematical Society》1999,127(2):599-608
In this paper, the central limit theorem for lacunary trigonometric series is proved. Two gap conditions by Erdos and Takahashi are extended and unified. The criterion for the Fourier character of lacunary series is also given.
12.
13.
Chern-Ching Chao 《Random Structures and Algorithms》1997,10(3):323-332
A unified martingale approach is presented for establishing the asymptotic normality of some sequences of random variables. It is applied to the numbers of inversions, rises, and peaks, respectively, as well as the oscillation and the sum of consecutive pair products of a random permutation. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 10, 323–332 (1997) 相似文献
14.
Hong Yan Sun 《数学学报(英文版)》2014,30(1):69-78
We establish a central limit theorem for a branching Brownian motion with random immigration under the annealed law,where the immigration is determined by another branching Brownian motion.The limit is a Gaussian random measure and the normalization is t3/4for d=3 and t1/2for d≥4,where in the critical dimension d=4 both the immigration and the branching Brownian motion itself make contributions to the covariance of the limit. 相似文献
15.
Let {Sn, n ≥ 1} be partial sums of independent identically distributed random variables. The almost sure version of CLT is generalized on the case of randomly indexed sums {SNn, n ≥ 1}, where {Nn, n ≥ 1} is a sequence of positive integer‐valued random variables independent of {Sn, n ≥ 1}. The affects of nonrandom centering and norming are considered too (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
Let T:X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f:X → Rd is a Hlder continuous function with ∫Xfdm = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ2:=σ2 (f ) such that Sfn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ2 . Moreover, there exists a real number A > 0 such that, for any integer n ≥ 1,Π( m*( 1√ nS f n ),N (0,σ2 ) ≤A√n, where m*(1√ n Sfn)denotes the distribution of 1√ n Sfn with respect to m, and Π is the Prokhorov metric. 相似文献
17.
The main result is that the necessary and sufficient conditions for the central limit theorem for centered, second-order processes given by Giné and Zinn(6) can be obtained without any basic measurability condition. Furthermore we extend some of their results. 相似文献
18.
A. Mačiulis 《Lithuanian Mathematical Journal》1999,39(1):58-63
The convergence of the value distributions of a normalized sequence of strongly additive arithmetic functions to the standard normal law in theL p metric is considered. An asymptotic formula for the variance is obtained. In both cases, the remainders are expressed in terms of the third absolute moment of the additive function. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 74–80, January–March, 1999. Translated by A. Mačiulis 相似文献
19.
C. Villegas 《Stochastic Processes and their Applications》1976,4(2):121-133
In 1957, Parzen proved a central limit theorem for a class of scalar processes which he called multilinear processes. In the present paper only stationary bilinear processes are considered, but the theory is generalized to the multivariate case. 相似文献
20.
Let
n
and
be an empirical process and a generalized Brownian bridge, respectively, indexed by a class of real measurable functions. From the central limit theorem for empirical processes it follows that for allr0. In this paper, assuming the class to be countably determined, under certain conditions we obtain an estimate for some constantC. Vapnik-ervonenkis class and the indicators of lower left orthants provide examples of classes considered here. 相似文献