共查询到20条相似文献,搜索用时 15 毫秒
1.
A random functional central limit theorem is obtained for processes of partial sums and product sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding results on processes of partial sums of linear processes generated by strictly stationary martingale differences, which can be found in [5]. 相似文献
2.
Florence Merlevède 《Stochastic Processes and their Applications》2012,122(1):170-190
In this paper, we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale with stationary differences. The results are exploited to further investigate the central limit theorem and its invariance principle started at a point, the almost sure central limit theorem, as well as the law of the iterated logarithm via almost sure approximation with a Brownian motion, improving the results available in the literature. The conditions are well suited for a variety of examples; they are easy to verify, for instance, for linear processes and functions of Bernoulli shifts. 相似文献
3.
Eric Slud 《Probability Theory and Related Fields》1991,87(3):349-364
Summary This paper applies the stochastic calculus of multiple Wiener-Itô integral expansions to express the number of crossings of the mean level by a stationary (discrete- or continuous-time) Gaussian process within a fixed time interval [0,T]. The resulting expansions involve a class of hypergeometric functions, for which recursion and differential relations and some asymptotic properties are derived. The representation obtained for level-crossing counts is applied to prove a central limit theorem of Cuzick (1976) for level crossings in continuous time, using a general central limit theorem of Chambers and Slud (1989a) for processes expressed via multiple Wiener-Itô integral expansions in terms of a stationary Gaussian process. Analogous results are given also for discrete-time processes. This approach proves that the limiting variance is strictly positive, without additional assumptions needed by Cuzick.Research supported by Office of Naval Research contracts N00014-86-K-0007 and N00014-89-J-1051 相似文献
4.
M. S. Ginovian 《Probability Theory and Related Fields》1994,100(3):395-406
Summary A central limit theorem for Toeplitz type quadratic functionals of a stationary Gaussian processX(t),t, is proved, generalizing the result of Avram [1] for discrete time processes. The result is applied to the problem of nonparametric estimation of linear functionals of an unknown spectral density function. We give some upper bounds for the minimax mean square risk of the nonparametric estimators, similar to those by Ibragimov and Has'minskii [12] for a probability density function. 相似文献
5.
Wei Biao Wu 《Proceedings of the American Mathematical Society》2005,133(1):285-293
We consider the asymptotic behavior of Fourier transforms of stationary and ergodic sequences. Under sufficiently mild conditions, central limit theorems are established for almost all frequencies as well as for a given frequency. Applications to the widely used linear processes and iterated random functions are discussed. Our results shed new light on the foundation of spectral analysis in that the asymptotic distribution of the periodogram, the fundamental quantity in the frequency-domain analysis, is obtained.
6.
We present a probabilistic analysis of two Krylov subspace methods for solving linear systems. We prove a central limit theorem for norms of the residual vectors that are produced by the conjugate gradient and MINRES algorithms when applied to a wide class of sample covariance matrices satisfying some standard moment conditions. The proof involves establishing a four-moment theorem for the so-called spectral measure, implying, in particular, universality for the matrix produced by the Lanczos iteration. The central limit theorem then implies an almost-deterministic iteration count for the iterative methods in question. © 2022 Wiley Periodicals LLC. 相似文献
7.
Zbyněk Pawlas 《Methodology and Computing in Applied Probability》2014,16(2):295-309
This paper is devoted to planar stationary line segment processes. The segments are assumed to be independent, identically distributed, and independent of the locations (reference points). We consider a point process formed by self-crossing points between the line segments. Its asymptotic variance is explicitly expressed for Poisson segment processes. The main result of the paper is the central limit theorem for the number of intersection points in expanding rectangular sampling window. It holds not only for Poisson processes of reference points but also for stationary point processes satisfying certain conditions on absolute regularity (β-mixing) coefficients. The proof is based on the central limit theorem for β-mixing random fields. Approximate confidence intervals for the intensity of intersections can be constructed. 相似文献
8.
The stationary density of an invertible linear processes can be estimated at the parametric rate by a convolution of residual-based
kernel estimators. We have shown elsewhere that the convergence is uniform and that a functional central limit theorem holds
in the space of continuous functions vanishing at infinity. Here we show that analogous results hold in weighted L
1-spaces. We do not require smoothness of the innovation density.
相似文献
9.
Povilas Banys 《Lithuanian Mathematical Journal》2011,51(3):303-309
In [V. Paulauskas, On Beveridge–Nelson decomposition and limit theorems for linear random fields, J. Multivariate Anal., 101:621–639, 2010], limit theorems for linear random fields generated by independent identically distributed innovations
were proved. In this paper, we present the central limit theorem for linear random fields with martingale-differences innovations
satisfying the central limit theorem from [J. Dedecker, A central limit theorem for stationary random fields, Probab. Theory Relat. Fields, 110(3):397–426, 1998] and arranged in lexicographical order. 相似文献
10.
The central limit theorem for Markov chains with normal transition operators, started at a point 总被引:2,自引:0,他引:2
The central limit theorem and the invariance principle, proved by Kipnis and Varadhan for reversible stationary ergodic Markov
chains with respect to the stationary law, are established with respect to the law of the chain started at a fixed point,
almost surely, under a slight reinforcing of their spectral assumption. The result is valid also for stationary ergodic chains
whose transition operator is normal.
Received: 28 March 2000 / Revised version: 25 July 2000 /?Published online: 15 February 2001 相似文献
11.
V. P. Demichev 《Mathematical Notes》2014,95(1-2):191-201
Integrals with respect to stationary random measures are considered. A central limit theorem for such integrals is proved. The results are applied to obtain a functional central limit theorem for transformed solutions of the Burgers equation with random initial data. 相似文献
12.
Mohsen Pourahmadi 《Journal of multivariate analysis》1983,13(1):177-186
The notion of sampling for second-order q-variate processes is defined. It is shown that if the components of a q-variate process (not necessarily stationary) admits a sampling theorem with some sample spacing, then the process itself admits a sampling theorem with the same sample spacing. A sampling theorem for q-variate stationary processes, under a periodicity condition on the range of the spectral measure of the process, is proved in the spirit of Lloy's work. This sampling theorem is used to show that if a q-variate stationary process admits a sampling theorem, then each of its components will admit a sampling theorem too. 相似文献
13.
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
14.
Yoshihide Kakizawa 《Journal of multivariate analysis》2007,98(5):992-1017
Moderate deviations limit theorem is proved for quadratic forms in zero-mean Gaussian stationary processes. Two particular cases are the cumulative periodogram and the kernel spectral density estimator. We also derive the exponential decay of moderate deviation probabilities of goodness-of-fit tests for the spectral density and then discuss intermediate asymptotic efficiencies of tests. 相似文献
15.
The central result is a limit theorem for not necessarily stationary processes resembling AR (p). Assumption of a vector limit distribution for standardized sample autocorrelations leads to the convergence of a vector limit distribution for ordinary sample partial autocorrelations, and to a clear relationship between the two limit distributions. The motivation is the study of the case p=1 by Mills and Seneta (1989, Stochastic Process Appl., 33, 151–161). The central result is used to explain the nature of the relationship between the two results of Quenouille in the classical stationary AR (p) setting. 相似文献
16.
As an extension of earlier papers on stationary sequences, a concept of weak dependence for strictly stationary random fields is introduced in terms of so-called homoclinic transformations. Under assumptions made within the framework of this concept a form of the almost sure central limit theorem (ASCLT) is established for random fields arising from a class of algebraic Z
d
-actions on compact abelian groups. As an auxillary result, the central limit theorem is proved via Ch. Stein's method. The next stage of the proof includes some estimates which are specific for ASCLT. Both steps are based on making use of homoclinic transformations. 相似文献
17.
This paper deals with so-called general linear stochastic processes (GLSP), defined by T. Kawata in 1972 in generalization of work of R. Lugannani and J. B. Thomas of 1967/71. These second order processes (which are not necessarily stationary nor have independent increments) are described by rather weak requirements, so that several processes such as some random noise and pulse train processes are specific models of these GLSP. Part I is concerned with two general theorems giving asymptotic expansions (including those for the density function) in the central limit theorem for such GLSP, together with error rates. The assumptions for the corresponding θ– and o–error estimates seem rather natural: in the former, apart from assumptions on the inherent structure of such GLSP, the existence of certain moments of higher order as well as a Cramer-type condition are assumed, in the latter in addition a Lindeberg-type condition of higher order. Fourier analytic machinery is used for the proofs. 相似文献
18.
Richard C Bradley 《Journal of multivariate analysis》1981,11(1):1-16
This article is motivated by a central limit theorem of Ibragimov for strictly stationary random sequences satisfying a mixing condition based on maximal correlations. Here we show that the mixing condition can be weakened slightly, and construct a class of stationary random sequences covered by the new version of the theorem but not Ibragimov's original version. Ibragimov's theorem is also extended to triangular arrays of random variables, and this is applied to some kernel-type estimates of probability density. 相似文献
19.
The increment ratio (IR) statistic was first defined and studied in Surgailis et al. (2007) [19] for estimating the memory parameter either of a stationary or an increment stationary Gaussian process. Here three extensions are proposed in the case of stationary processes. First, a multidimensional central limit theorem is established for a vector composed by several IR statistics. Second, a goodness-of-fit χ2-type test can be deduced from this theorem. Finally, this theorem allows to construct adaptive versions of the estimator and the test which are studied in a general semiparametric frame. The adaptive estimator of the long-memory parameter is proved to follow an oracle property. Simulations attest to the interesting accuracies and robustness of the estimator and the test, even in the non Gaussian case. 相似文献
20.
Jérôme Dedecker Florence Merlevède Dalibor Volný 《Journal of Theoretical Probability》2007,20(4):971-1004
In this paper we study the central limit theorem and its weak invariance principle for sums of non-adapted stationary sequences,
under different normalizations. Our conditions involve the conditional expectation of the variables with respect to a given
σ-algebra, as done in Gordin (Dokl. Akad. Nauk SSSR 188, 739–741, 1969) and Heyde (Z. Wahrsch. verw. Gebiete 30, 315–320, 1974). These conditions are well adapted to a large variety of examples, including linear processes with dependent innovations
or regular functions of linear processes. 相似文献