共查询到20条相似文献,搜索用时 31 毫秒
1.
Let (Xn)n? be a sequence of real, independent, not necessarily identically distributed random variables (r.v.) with distribution functions FXn, and Sn = Σi=1nXi. The authors present limit theorems together with convergence rates for the normalized sums ?(n)Sn, where ?: → +, ?(n) → 0, n → ∞, towards appropriate limiting r.v. X, the convergence being taken in the weak (star) sense. Thus higher order estimates are given for the expression ∝f(x) d[F?(n)Sn(x) ? FX(x)] which depend upon the normalizing function ?, decomposability properties of X and smoothness properties of the function f under consideration. The general theorems of this unified approach subsume O- and o-higher order error estimates based upon assumptions on associated moments. These results are also extended to multi-dimensional random vectors. 相似文献
2.
Harry E Hürzeler 《Journal of multivariate analysis》1984,14(1):34-73
The concept of a quasimartingale, and therefore also of a function of bounded variation, is extended to processes with a regular partially ordered index set V and with values in a Banach space. We show that quasimartingales can be described by their associated measures, defined on an inverse limit space containing , furnished with the σ-algebra of the predictable sets. With the help of this measure, a Rao-Krickeberg and a Riesz decomposition is obtained, as well as a convergence theorem for quasimartingales. For a regular quasimartingale X it is proven that the spaces (, ) and the measures associated with X are unique up to isomorphisms. In the case V = +n we prove a duality between classical (right-) quasimartingales and left-quasimartingales. 相似文献
3.
Norbert Herrndorf 《Journal of multivariate analysis》1984,15(1):141-146
In this note a functional central limit theorem for ?-mixing sequences of I. A. Ibragimov (Theory Probab. Appl.20 (1975), 135–141) is generalized to nonstationary sequences (Xn)n ∈ , satisfying some assumptions on the variances and the moment condition for some b > 0, ? > 0. 相似文献
4.
F. Götze 《Journal of multivariate analysis》1985,16(1):1-20
Asymptotic expansions for a class of functional limit theorems are investigated. It is shown that the expansions in this class fit into a common scheme, defined by a sequence of functions hn (ε1,…, εn), n ≥ 1, of “weights” (for n observations), which are smooth, symmetric, compatible and have vanishing first derivatives at zero. Then admits an asymptotic expansion in powers of . Applications to quadratic von Mises functionals, the C.L.T. in Banach spaces, and the invariance principle are discussed. 相似文献
5.
B值随机变量序列的局部收敛定理 总被引:3,自引:0,他引:3
本文的目的是研究B值随机变量序列的局部收敛定理。作为推论,得到了一类B值鞅差序列的极限定理和若干经典的独立随机变量序列的极限定理。 相似文献
6.
7.
P. Masani 《Journal of multivariate analysis》1977,7(2):292-335
We extend the Lévy inversion formula for the recovery of a bounded measure over from its Fourier-Stieltjes transform to bounded complex-valued, orthogonally scattered Hilbert space-valued, and spectral projection operator-valued measures over any first countable locally compact Abelian group. All our results are direct generalizations of known inversions for . 相似文献
8.
Convergence of weighted sums of tight random elements {Vn} (in a separable Banach space) which have zero expected values and uniformly bounded rth moments (r > 1) is obtained. In particular, if {ank} is a Toeplitz sequence of real numbers, then | Σk=1∞ankf(Vk)| → 0 in probability for each continuous linear functional f if and only if 6Σk=1∞ankVk 6→ 0 in probability. When the random elements are independent and max1≤k≤n | ank | = (n?8) for some , then |Σk=1∞ankVk 6→ 0 with probability 1. These results yield laws of large numbers without assuming geometric conditions on the Banach space. Finally, these results can be extended to random elements in certain Fréchet spaces. 相似文献
9.
Let (Ω, , μ) be a finite measure space and a real separable Banach space. Measurability and integrability are defined for multivalued functions on Ω with values in the family of nonempty closed subsets of . To present a theory of integrals, conditional expectations, and martingales of multivalued functions, several types of spaces of integrably bounded multivalued functions are formulated as complete metric spaces including the space L1(Ω; ) isometrically. For multivalued functions in these spaces, multivalued conditional expectations are introduced, and the properties possessed by the usual conditional expectation are obtained for the multivalued conditional expectation with some modifications. Multivalued martingales are also defined, and their convergence theorems are established in several ways. 相似文献
10.
G.Y.H Chi 《Journal of multivariate analysis》1973,3(1):71-92
Let (Ω, Σ, P) be a fixed complete probability space, the real Schwartz space, and its strong dual. and are partially ordered by and respectively, where is the positive cone of nonnegative functions in and its dual in . is a strict -cone and is normal, where is the family of all bounded subsets of . If X, Y are two random Schwartz distributions, then X ≤ Y if and only if Y(ω) ? X(ω) ∈ for almost all . Integrability of random Schwartz distributions and properties of such integrals are discussed. The monotone convergence theorem, the dominated convergence theorem, and Fatou's lemma are proved. The existence of conditional expectations of integrable random Schwartz distributions relative to a given sub σ-field of Σ is shown. Properties of conditional expectations are discussed and the conditional form of the monotone convergence theorem is proved. Sub(super)-martingale sequences are defined via the partial order relations introduced above, and a convergence theorem is given. The notion of a potential is introduced and the Riesz decomposition theorem is proved. 相似文献
11.
If X is a point random field on d then convergence in distribution of the renormalization Cλ|Xλ ? αλ| as λ → ∞ to generalized random fields is examined, where Cλ > 0, αλ are real numbers for λ > 0, and Xλ(f) = λ?dX(fλ) for . If such a scaling limit exists then Cλ = λθg(λ), where g is a slowly varying function, and the scaling limit is self-similar with exponent θ. The classical case occurs when and the limit process is a Gaussian white noise. Scaling limits of subordinated Poisson (doubly stochastic) point random fields are calculated in terms of the scaling limit of the environment (driving random field). If the exponent of the scaling limit is then the limit is an independent sum of the scaling limit of the environment and a Gaussian white noise. If the scaling limit coincides with that of the environment while if the limit is Gaussian white noise. Analogous results are derived for cluster processes as well. 相似文献
12.
E. Bolthausen 《Stochastic Processes and their Applications》1979,9(2):217-222
Let Xn be an irreducible aperiodic recurrent Markov chain with countable state space I and with the mean recurrence times having second moments. There is proved a global central limit theorem for the properly normalized sojourn times. More precisely, if , then the probability measures induced by {t(n)i/√n?√nπi}i?I(πi being the ergotic distribution) on the Hilbert-space of square summable I-sequences converge weakly in this space to a Gaussian measure determined by a certain weak potential operator. 相似文献
13.
Helmut Strasser 《Journal of multivariate analysis》1975,5(2):206-226
Let (X, ) be a measurable space, Θ ? an open interval and PΩ ∥ , Ω ? Θ, a family of probability measures fulfilling certain regularity conditions. Let be the maximum likelihood estimate for the sample size n. Let λ be a prior distribution on Θ and let be the posterior distribution for the sample size n given . denotes a loss function fulfilling certain regularity conditions and Tn denotes the Bayes estimate relative to λ and L for the sample size n. It is proved that for every compact K ? Θ there exists cK ≥ 0 such that This theorem improves results of Bickel and Yahav [3], and Ibragimov and Has'minskii [4], as far as the speed of convergence is concerned. 相似文献
14.
Mou-Hsiung Chang 《Journal of multivariate analysis》1979,9(3):434-441
Let {W(t): t ≥ 0} be μ-Brownian motion in a real separable Banach space B, and let aT be a nondecreasing function of T for which (i) 0 < aT ≤ T (T ≥ 0), (ii) is nonincreasing. We establish a Strassen limit theorem for the net {ξT: T ≥ 3}, where 相似文献
15.
Jack W Silverstein 《Journal of multivariate analysis》1984,15(3):295-324
Let {vij} i,j = 1, 2,…, be i.i.d. standardized random variables. For each n, let Vn = (vij) i = 1, 2,…, n; j = 1, 2,…, s = s(n), where as n → ∞, and let . Previous results [7, 8] have shown the eigenvectors of Mn to display behavior, for n large, similar to those of the corresponding Wishart matrix. A certain stochastic process Xn on [0, 1], constructed from the eigenvectors of Mn, is known to converge weakly, as n → ∞, on D[0, 1] to Brownian bridge when v11 is N(0, 1), but it is not known whether this property holds for any other distribution. The present paper provides evidence that this property may hold in the non-Wishart case in the form of limit theorems on the convergence in distribution of random variables constructed from integrating analytic function w.r.t. Xn(Fn(x)), where Fn is the empirical distribution function of the eigenvalues of Mn. The theorems assume certain conditions on the moments of v11 including E(v114) = 3, the latter being necessary for the theorems to hold. 相似文献
16.
Richard C Bradley 《Journal of multivariate analysis》1983,13(1):167-176
The maximal correlation between a pair of σ-fields and becomes arbitrarily small as sup{|P(A ? B) ? P(A) P(B)|/[P(A) P(B)]1/2, A ∈ , B ∈ , P(A) > 0, P(B) > 0} becomes sufficiently small. 相似文献
17.
On the convergence of vector random measures 总被引:4,自引:0,他引:4
Dang Hung Thang 《Probability Theory and Related Fields》1991,88(1):1-16
Summary The aim of this paper is to study Banach space-valued symmetric independently scattered random measures with emphasis on their convergence properties. The Vitali-Hahn-Saks Theorem, the Skorokhod theorem about the relations between the convergence a.e. and the convergence in law of random variables, and the central limit theorem for Banach valued random variables due to Hoffmann-Jorgensen, Pisier are extended to such measures. 相似文献
18.
This part is concerned with the applications of the general limit theorems with rates of Part I, achieved by specializing the limiting r.v. X. This leads to new convergence theorems with higher order rates in the one- and multi-dimensional case for the stable limit law, for the central limit theorem, and the weak law of large numbers. 相似文献
19.
Let be the Schwartz space of rapidly decreasing real functions. The dual space 1 consists of the tempered distributions and the relation ? L2() ? 1 holds. Let γ be the Gaussian white noise on 1 with the characteristic functional , ξ ∈ , where ∥·∥ is the L2()-norm. Let ν be the Poisson white noise on 1 with the characteristic functional = exp?∫ {[exp(iξ(t)u)] ? 1 ? (1 + u2)?1(iξ(t)u)} dη(u)dt), ξ ∈ , where the Lévy measure is assumed to satisfy the condition ∫u2dη(u) < ∞. It is proved that γ1ν has the same dichotomy property for shifts as the Gaussian white noise, i.e., for any ω ∈ 1, the shift of γ1ν by ω and γ1ν are either equivalent or orthogonal. They are equivalent if and only if when ω ∈ L2() and the Radon-Nikodym derivative is derived. It is also proved that for the Poisson white noice νω is orthogonal to ν for any non-zero ω in 1. 相似文献
20.
Ibrahim A Ahmad 《Journal of multivariate analysis》1979,9(2):314-321
In this note we obtain rates of convergence in the central limit theorem for certain maximum of coordinate partial sums of independent identically distributed random vectors having positive mean vector and a nonsingular correlation matrix. The results obtained are in terms of rates of convergence in the multidimensional central limit theorem. Thus under the conditions of Sazonov (1968, Sankhya, Series A30 181–204, Theorem 2), we have the same rate of convergence for the vector of coordinate maximums. Other conditions for the multidimensional CLT are also discussed, c.f., Bhattachaya (1977, Ann. Probability 5 1–27). As an application of one of the results we obtain a multivariate extension of a theorem of Rogozin (1966, Theor. Probability Appl. 11 438–441). 相似文献