共查询到20条相似文献,搜索用时 31 毫秒
1.
本文研究了多维随机向量序列加权和的渐近行为.利用Lindeberg中心极限定理的基本思想,得到了多维随机向量序列加权和的中心极限定理及其收敛速度,为Lindeberg中心极限定理的推广. 相似文献
2.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》2001,332(8):761-764
In this Note we obtain a central limit theorem for standard kernel invariant density estimates of one-dimensional dynamical systems. The two main steps in the proof of this theorem are the following: the study of speed of convergence for the variance of the estimator and then a variation on the Lindeberg–Rio method [6]. 相似文献
3.
In this paper we extend a central limit theorem of Peligrad for uniformly strong mixing random fields satisfying the Lindeberg condition in the absence of stationarity property. More precisely, we study the asymptotic normality of the partial sums of uniformly \(\alpha \)-mixing non-stationary random fields satisfying the Lindeberg condition, in the presence of an extra dependence assumption involving maximal correlations. 相似文献
4.
Lixin Zhang 《数学学报(英文版)》2000,16(4):691-710
Abstract
The aim of this paper is to investigate the central limit theorems for asymptotically negatively dependent random fields under
lower moment conditions or the Lindeberg condition. Results obtained improve a central limit theorem of Roussas [11] for negatively
assiated fields and the main results of Su and Chi [18], and also include a central limit of theorem for weakly negatively
associated random variables similar to that of Burton et al. [20].
Research supported by National Natural Science Foundation of China (No. 19701011) 相似文献
5.
《Stochastic Processes and their Applications》2001,94(1):105-134
The discovery of the almost sure central limit theorem (Brosamler, Math. Proc. Cambridge Philos. Soc. 104 (1988) 561–574; Schatte, Math. Nachr. 137 (1988) 249–256) revealed a new phenomenon in classical central limit theory and has led to an extensive literature in the past decade. In particular, a.s. central limit theorems and various related ‘logarithmic’ limit theorems have been obtained for several classes of independent and dependent random variables. In this paper we extend this theory and show that not only the central limit theorem, but every weak limit theorem for independent random variables, subject to minor technical conditions, has an analogous almost sure version. For many classical limit theorems this involves logarithmic averaging, as in the case of the CLT, but we need radically different averaging processes for ‘more sensitive’ limit theorems. Several examples of such a.s. limit theorems are discussed. 相似文献
6.
《Stochastic Processes and their Applications》2020,130(3):1426-1434
We give error estimates in Peng’s central limit theorem for not necessarily nondegenerate case. The exposition uses the language of the classical probability theory instead of the language of the theory of sublinear expectations. We only consider the one-dimensional case. The higher dimensional extension is left to the interested reader. 相似文献
7.
Dirk Zeindler 《Journal of Theoretical Probability》2013,26(4):968-996
Hambly, Keevash, O’Connell, and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on the symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance. 相似文献
8.
Under some weaker conditions, we give a central limit theorem under sublinear expectations, which extends Peng’s central limit theorem. 相似文献
9.
It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost 1/n can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein’s method of exchangeable pairs. 相似文献
10.
Aurel Spătaru 《Statistics & probability letters》2010,80(21-22):1680-1683
We prove a central limit theorem for a renewal process based on a sequence of independent non-negative interarrival times whose distributions are taken from a finite set. The result extends the classical central limit theorem obtained by Takács (1956). 相似文献
11.
Greg Kuperberg 《Transactions of the American Mathematical Society》2005,357(2):459-471
We prove a central limit theorem for non-commutative random variables in a von Neumann algebra with a tracial state: Any non-commutative polynomial of averages of i.i.d. samples converges to a classical limit. The proof is based on a central limit theorem for ordered joint distributions together with a commutator estimate related to the Baker-Campbell-Hausdorff expansion. The result can be considered a generalization of Johansson's theorem on the limiting distribution of the shape of a random word in a fixed alphabet as its length goes to infinity.
12.
An existence theorem of a positive solution to a semipositone Sturm–Liouville boundary value problem
Qingliu Yao 《Applied Mathematics Letters》2010,23(12):1401-1406
We study a positive solution of the semipositone Sturm-Liouville boundary value problem in which the nonlinear term has no numerical lower bound. By considering the integration of certain limit growth functions and applying the Krasnosel’skii fixed point theorem on a cone, an existence theorem is proved, and a classical existence result is extended by this theorem. 相似文献
13.
Maxim Derevyagin Olga Holtz Sergey Khrushchev Mikhail Tyaglov 《Journal of Approximation Theory》2012,164(9):1238-1261
We extend some classical theorems in the theory of orthogonal polynomials on the unit circle to the matrix case. In particular, we prove a matrix analogue of Szeg?’s theorem. As a by-product, we also obtain an elementary proof of the distance formula by Helson and Lowdenslager. 相似文献
14.
本文在{ξi}为强混合样本,{ani}是实三角阵列下,得到了一个新的关于线性和n∑i=1aniξi的中心极限定理.并利用该中心极限定理,进一步建立了线性过程部分和的中心极限定理. 相似文献
15.
《Stochastic Processes and their Applications》2020,130(3):1820-1852
We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of stochastic gradient descent training iterations. Our result describes the neural network’s fluctuations around its mean-field limit. The fluctuations have a Gaussian distribution and satisfy a stochastic partial differential equation. The proof relies upon weak convergence methods from stochastic analysis. In particular, we prove relative compactness for the sequence of processes and uniqueness of the limiting process in a suitable Sobolev space. 相似文献
16.
This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order whose derivative satisfies some growth condition at ∞. This class contains most of the classical families of transcendental functions and goes much beyond. Based on uniform versions of Nevanlinna’s value distribution theory, we first build a thermodynamical formalism which, in particular, produces unique geometric and fiberwise invariant Gibbs states. Moreover, spectral gap property for the associated transfer operator along with exponential decay of correlations and a central limit theorem are shown. This part relies on our construction of new positive invariant cones that are adapted to the setting of unbounded phase spaces. This setting rules out the use of Hilbert’s metric along with the usual contraction principle. However, these cones allow us to apply a contraction argument stemming from Bowen’s initial approach. 相似文献
17.
A central limit theorem for strong mixing sequences is given that applies to both non-stationary sequences and triangular array settings. The result improves on an earlier central limit theorem for this type of dependence given by Politis, Romano and Wolf in 1997. 相似文献
18.
We present a Darboux-Wiener type lemma as a powerful alternative to the classical Tauberian theorem when monotonicity is not
known a priori. We apply it to obtain the exact asymptotics of the variance of the self-intersections of a one-dimensional
stable random walk. Finally we prove a functional central limit theorem for stable random walk in random scenery conjectured
in [1]. 相似文献
19.
We prove a stable version of the Lindeberg–Feller theorem and apply this result to an approximation of stable processes that are represented by stochastic integrals. 相似文献
20.
Max Skipper 《Statistics & probability letters》2010,80(9-10):771-778
We show that almost any one-dimensional projection of a suitably scaled random walk on a hypercube, inscribed in a hypersphere, converges weakly to an Ornstein–Uhlenbeck process as the dimension of the sphere tends to infinity. We also observe that the same result holds when the random walk is replaced with spherical Brownian motion. This latter result can be viewed as a “functional” generalisation of Poincaré’s observation for projections of uniform measure on high dimensional spheres; the former result is an analogous generalisation of the Bernoulli–Laplace central limit theorem. Given the relation of these two classic results to the central limit theorem for convex bodies, the modest results provided here would appear to motivate a functional generalisation. 相似文献