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Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} ${\cal {X}}_{n} =(X_1,\ldots,X_n)$ \end{document} be a random vector. Suppose that the random variables \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $(X_i)_{1\leq i\leq n}$ \end{document} are stationary and fulfill a suitable dependence criterion. Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $f$ \end{document} be a real valued function defined on \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathbbm{R}^n$ \end{document} having some regular properties. Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} ${\cal {Y}}_{n}$ \end{document} be a random vector, independent of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} ${\cal {X}}_{n}$ \end{document}, having independent and identically distributed components. We control \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\left|\mathbbm{E}(f({\cal {X}}_{n}))-\mathbbm{E} (f({\cal {Y}}_{n}))\right|$ \end{document}. Suitable choices of the function \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $f$ \end{document} yield, under minimal conditions, to rates of convergence in the central limit theorem, to some moment inequalities or to bounds useful for Poisson approximation. The proofs are derived from multivariate extensions of Taylor's formula and of the Lindeberg decomposition. In the univariate case and in the mixing setting the method is due to Rio (1995).

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central limit theorem, Arch. Math. , 43 (1984), no. 3, pp. 258–264. MR 0766433 ( 86a :60029) Walter G. G. A fixed point theorem and its application to the central limit theorem

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Mathematicum , 10 ( 6 ) ( 1998 ), 687 – 698 . [2] Baez-Duarte , L. , Central limit theorem for complex measures , Journal of

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. [10] Peligrad , M. 1987 On the central limit theorem for ρ -mixing sequences of random variables Ann. Probab. 15 1387 – 1394 10.1214/aop

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. 8 361 386 ACOSTA, A. DE, Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm

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. 22 1044 1077 EGOROV, V. A., On a central limit theorem with random normalization, Rings and modules. Limit theorems of probability theory , No. 1

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and uses averages on the assumption of the Central Limit Theorem (Glänzel 2010 ). However, citation distributions are extremely skewed (Seglen 1992 , 1997 ; cf. Leydesdorff 2008 ) and central tendency statistics give misleading results. Using

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. , & Clark , J. ( 2003 ). Successful students’ conceptions of mean, standard deviation, and the Central Limit Theorem (Unpublished paper). Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.446.6077&rep=rep1&type

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that its variance changes with time. For the case β = 0 the central limit theorem tells us that the variance should scale as σ 2 ∼ t −1 where t denotes the number of elapsed time steps. This would be manifested in a systematic temporal variation in

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