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Abstract  

By applying the Skorohod martingale embedding method, a strong approximation theorem for partial sums of asymptotically negatively dependent (AND) Gaussian sequences, under polynomial decay rates, is established. As applications, the law of the iterated logarithm, the Chung-type law of the iterated logarithm and the almost sure central limit theorem for AND Gaussian sequences are derived.

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Abstract  

We show that as processes in (c, d, t) ∈ C(R 2 × R + 1)

\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} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{{\int_c^d {(L_t^{x + h} - L_t^x )^2 dx - 4h} \int_c^d {L_t^x dx} }} {{h^{3/2} }}\mathop \Rightarrow \limits^\mathcal{L} \left( {\frac{{64}} {3}} \right)^{1/2} \int_c^d {L_t^x d\eta (x)}$$ \end{document}
as h → 0 for Brownian local time L t x. Here η(x) is an independent two-sided Brownian motion.

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Abstract  

Let Y s,n denote the number of part sizes ≧ s in a random and uniform partition of the positive integer n that are counted without multiplicity. For s = λ(6n)1/2/π + o(n 1/4), 0 ≦ λ < ∞, as n → ∞, we establish the weak convergence of Y s,n to a Gaussian distribution in the form of a central limit theorem. The mean and the standard deviation are also asymptotically determined.

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Abstract  

We give a new proof of the central limit theorem for one dimensional symmetric random walk in random environment. The proof is quite elementary and natural. We show the convergence of the generators and from this we conclude the convergence of the process. We also investigate the hydrodynamic limit (HDL) of one dimensional symmetric simple exclusion in random environment and prove stochastic convergence of the scaled density field. The macroscopic behaviour of this field is given by a linear heat equation. The diffusion coefficient is the same as that of the corresponding random walk.

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Summary This article provides a glimpse of some of the highlights of the joint work of Endre Csáki and Pál Révész since 1979.  The topics of this short exploration of the rich stochastic milieu of this inspiring collaboration revolve around Brownian motion, random walks and their long excursions, local times and additive functionals, iterated processes, almost sure local and global central limit theorems, integral functionals of geometric stochastic processes, favourite sites--favourite values and jump sizes for random walk and Brownian motion, random walking in a random scenery, and large void zones and occupation times for coalescing random walks.

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References [1] Berkes , I. 1978 On the central limit theorem for lacunary trigonometric series Anal. Math

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BERKES, I., On the almost sure central limit theorem and domains of attraction, Probab. Theory Related Fields 102 (1995), 1-17. MR 96j :60033 On the almost sure central limit theorem and domains of attraction

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Abstract  

Let {(X nk, 1≤kn),n≥1}, be an array of rowwise independent random variables. We extend and generalize some recent results due to Hu, Mricz and Taylor concerning complete convergence, in the sense of Hsu and Robbins, of the sequence of rowwise arithmetic means.

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Abstract  

Modified least squares processes (MLSP’s) and self-randomized MLSP’s are introduced in D[0, 1] for the slope in linear structural and functional error-in-variables models (EIVM’s). Sup-norm approximations in probability and, as a consequence, functional central limit theorems (CLT’s) are established for the data-based self-normalized versions of these MLSP’s and self-randomized MLSP’s. The MLSP’s are believed to be new types of objects of study, and the invariance principles for them constitute new asymptotics, in EIVM’s. Moreover, the obtained data-based functional CLT’s for the MLSP’s open up new possibilities for constructing various asymptotic confidence intervals (CI’s) for the slope that are named functional asymptotic CI’s here. Three special examples of such CI’s are given.

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Why with bibliometrics the Humanities does not need to be the weakest link

Indicators for research evaluation based on citations, library holdings, and productivity measures

Scientometrics
Author: A. Linmans

Abstract  

In this study an attempt is made to establish new bibliometric indicators for the assessment of research in the Humanities. Data from a Dutch Faculty of Humanities was used to provide the investigation a sound empirical basis. For several reasons (particularly related to coverage) the standard citation indicators, developed for the sciences, are unsatisfactory. Target expanded citation analysis and the use of oeuvre (lifetime) citation data, as well as the addition of library holdings and productivity indicators enable a more representative and fair assessment. Given the skew distribution of population data, individual rankings can best be determined based on log transformed data. For group rankings this is less urgent because of the central limit theorem. Lifetime citation data is corrected for professional age by means of exponential regression.

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