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Xia Chen (2008)
Annales de l'I.H.P. Probabilités et statistiques
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In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy =∑ 1 of the polymer { , …, } equipped with random electrical charges { , …, }. Our approach is based on comparison of the moments between and the self-intersection local time =∑1 run by the...
Franciszek Czekała (1996)
Applicationes Mathematicae
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The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].
J. Meder (1958)
Annales Polonici Mathematici
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Carsten Schütt (1984)
Studia Mathematica
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Pierre Alquier (2008)
Annales de l'I.H.P. Probabilités et statistiques
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This paper presents a new algorithm to perform regression estimation, in both the inductive and transductive setting. The estimator is defined as a linear combination of functions in a given dictionary. Coefficients of the combinations are computed sequentially using projection on some simple sets. These sets are defined as confidence regions provided by a deviation (PAC) inequality on an estimator in one-dimensional models. We prove that every projection the algorithm actually improves...
Jérôme Dedecker, Emmanuel Rio (2008)
Annales de l'I.H.P. Probabilités et statistiques
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In this paper, we give estimates of the minimal distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.
Michael Drmota, Johannes Gajdosik (1998)
Journal de théorie des nombres de Bordeaux
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By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.