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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
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《Fuzzy Sets and Systems》1987,24(3):331-344
Fuzzy random variables have been proposed to treat situations in which both random behavior and fuzzy perception must be considered. A definition of independence is given for fuzzy random variables, as well as a notion of fuzzy Gaussian random variables. It is shown that a sum or mean of independent fuzzy random variables converges in the limit to a fuzzy Gaussian random variable, thus providing a fuzzy analogue of the central limit theorem of classical probability theory. 相似文献
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R.A. Maller 《Stochastic Processes and their Applications》1978,7(1):101-111
A local limit theorem is given for independent noninteger random variables under a condition which is more general than one previously given, and which reduces, in the case of identically distributed random variables, to a well-known result. 相似文献
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A random functional central limit theorem for martingales 总被引:2,自引:0,他引:2
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Zbigniew S. Szewczak 《Statistics & probability letters》2010,80(9-10):747-751
Residues of partial sums in a class of dependent random variables, including functionals of uniformly recurrent Markov chains, are in the domain of attraction of the uniform distribution. These types of limit theorems arise for example in the multiplication of floating-point numbers. 相似文献
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Jérôme Dedecker 《Probability Theory and Related Fields》1998,110(3):397-426
Summary. We prove a central limit theorem for strictly stationary random fields under a projective assumption. Our criterion is similar
to projective criteria for stationary sequences derived from Gordin's theorem about approximating martingales. However our
approach is completely different, for we establish our result by adapting Lindeberg's method. The criterion that it provides
is weaker than martingale-type conditions, and moreover we obtain as a straightforward consequence, central limit theorems
for α-mixing or φ-mixing random fields.
Received: 19 February 1997 / In revised form: 2 September 1997 相似文献
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This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form Xk=g(εk−s,s∈Zd), k∈Zd, where (εi)i∈Zd are iid random variables and g is a measurable function. Such kind of spatial processes provides a general framework for stationary ergodic random fields. Under a short-range dependence condition, we show that the central limit theorem holds without any assumption on the underlying domain on which the process is observed. A limit theorem for the sample auto-covariance function is also established. 相似文献
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We introduce a class of distribution-valued stochastic processes that arise in the study of pulse reflection from random media and we analyze their asymptotic properties when they are scaled in a natural way.This research was supported by the National Science Foundation under Grants DMS-8201895 and DMS-90003227. 相似文献
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In this paper, we prove a local limit theorem for the distribution of the number of triangles in the Erdos‐Rényi random graph G(n, p), where is a fixed constant. Our proof is based on bounding the characteristic function of the number of triangles, and uses several different conditioning arguments for handling different ranges of t. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 48, 732–750, 2016 相似文献
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 8, pp. 1064–1070, August, 1989. 相似文献
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刘文 《应用数学学报(英文版)》1996,12(3):328-331
ASTRONGLIMITTHEOREMFORGENERALIZEDCANTOR-LIKE RANDOM SEQUENCESLIUWEN(刘文)(DepartmentofMathematicsandPhysics,HebeiUniversityofTe... 相似文献
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Rolando Cavazos-Cadena Daniel Hernández-Hernández 《Periodica Mathematica Hungarica》2008,56(2):183-211
This note concerns the asymptotic behavior of a Markov process obtained from normalized products of independent and identically
distributed random matrices. The weak convergence of this process is proved, as well as the law of large numbers and the central
limit theorem.
This work was supported by the PSF Organization under Grant No. 2005-7-02, and by the Consejo Nacional de Ciencia y Tecnología
under Grants 25357 and 61423. 相似文献
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