共查询到20条相似文献,搜索用时 15 毫秒
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Roland Speicher 《Mathematische Zeitschrift》1992,209(1):55-66
This work has been supported by the Deutsche Forschungsgemeinschaft (SFB 123) 相似文献
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Sergey G. Bobkov Gennadiy P. Chistyakov Friedrich Götze 《Probability Theory and Related Fields》2014,159(1-2):1-59
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions. 相似文献
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Yu. V. Borovskikh 《Ukrainian Mathematical Journal》1989,41(2):240-242
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 2, pp. 269–271, February, 1989. 相似文献
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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.
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Ying-xuan Niu 《高校应用数学学报(英文版)》2009,24(2):230-236
Let X be a compact metric space studies some relationships between stochastic and f : X→ X be a continuous map. This paper and topological properties of dynamical systems. It is shown that if f satisfies the central limit theorem, then f is topologically ergodic and / is sensitively dependent on initial conditions if and only if / is neither minimal nor equicontinuous. 相似文献
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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
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M. I. Gordin 《Journal of Mathematical Sciences》1994,68(4):451-458
The definitions of homoclinic partitions and transformations are given in situations that are standard for topological dynamics and ergodic theory. A variant of the central limit theorem is proved, the formulation of which makes use of homoclinic transformations.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 80–91, 1990. 相似文献
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Aloisio Pessoa de Araujo 《Journal of multivariate analysis》1978,8(4):598-613
It is shown, with the use of a concentration inequality of LeCam, that associated with an infinitely divisible random variable with values in a separable Banach space there is a Lévy-Khintchine formula. A partial converse of this fact is also proved. Relations between the continuity of the compound Poisson and the Gaussian variables associated with a Lévy measure are studied. A central limit theorem is obtained and examples are given. 相似文献
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Let Xn, n
, be i.i.d. with mean 0, variance 1, and E(¦Xn¦r) < ∞ for some r 3. Assume that Cramér's condition is fulfilled. We prove that the conditional probabilities P(1/√n Σi = 1n Xi t¦B) can be approximated by a modified Edgeworth expansion up to order o(1/n(r − 2)/2)), if the distances of the set B from the σ-fields σ(X1, …, Xn) are of order O(1/n(r − 2)/2)(lg n)β), where β < −(r − 2)/2 for r
and β < −r/2 for r
. An example shows that if we replace β < −(r − 2)/2 by β = −(r − 2)/2 for r
(β < −r/2 by β = −r/2 for r
) we can only obtain the approximation order O(1/n(r − 2)/2)) for r
(O(lg lgn/n(r − 2)/2)) for r
). 相似文献
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Necessary and sufficient conditions for the functional central limit theorem for a double array of random variables are sought. It is argued that this is a martingale problem only if the variables truncated at some fixed point c are asymptotically a martingale difference array. Under this hypothesis, necessary and sufficient conditions for convergence in distribution to a Brownian motion are obtained when the normalization is given (i) by the sums of squares of the variables, (ii) by the conditional variances and (iii) by the variances. The results are proved by comparing the various normalizations with a natural normalization.Research sponsored in part by the Office of Naval Research, Contract N00014-75-C-0809 相似文献
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We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L2 spaces and Poincaré inequalities, to provide a better understanding of the decrease in Fisher information implied by results of Barron and Brown. We show that if the standardized Fisher information ever becomes finite then it converges to zero.OTJ is a Fellow of Christs College, Cambridge, who helped support two trips to Yale University during which this paper was written.Mathematics Subject Classification (2000):Primary: 62B10 Secondary: 60F05, 94A17 相似文献
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SU ZHONGGEN 《高校应用数学学报(英文版)》1995,10(4):367-378
ONTHECENTRALLIMITTHEOREMINPRODUCTSPACESSUZHONGGENAbstract:SupposethatEandFareseparableBanachspaces,XandYareindependentsymmetr... 相似文献
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Summary Let F
*n
denote the n th convolution of a distribution function F on R
k
and suppose that F has zero moments of the first order and finite second order moment matrix. It is well-known that F
*n
(n·) converges to a Gaussian d.f. as n + t8. These d.f.s determine measures F
*n
(nA) and (A) for Borelsets A, We present a method that admits the estimation of the remainder-term F
*n
(n A)- (A) when A belongs to a certain class of Borelsets. This class contains all convex sets. If F has finite absolute third order moments then the remainder-term is of the order n
–1/2. Also the remainder term's dependence on the dimension k is given. These results strengthen and generalize earlier results in the same direction.This paper was first communicated at the Scandinavian mathematical congress in Oslo, August 1968. 相似文献