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作者：Kallenberg, Olav
作者单位：Auburn University System; Auburn University
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作者：Chazottes, J.-R.; Gouezel, S.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universite de Rennes
摘要：The purpose of this article is to support the idea that whenever we can prove a limit theorem in the classical sense for a dynamical system, we can prove a suitable almost-sure version based on an empirical measure with log-average. We follow three different approaches: martingale methods, spectral methods and induction arguments. Our results apply, among others, to Axiom A maps or flows, to systems inducing a Gibbs-Markov map, and to the stadium billiard.
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作者：Mattner, Lutz; Roos, Bero
作者单位：University of Lubeck; University of Hamburg
摘要：We give a shorter proof of Kanter's (J. Multivariate Anal. 6, 222-236, 1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide sharp upper bounds for the sum of modified Bessel functions I-0(x) + I-1(x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent random variables due to Cekanavicius & Roos (Lith. Math. J. 46, 54-91, 2006); Roos (Bernoulli, 11, 533-557, 2005), Bar...
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作者：Cranston, M.; Molchanov, S.
作者单位：University of California System; University of California Irvine; University of North Carolina; University of North Carolina Charlotte
摘要：We study limit behavior for sums of the form 1/vertical bar Lambda(L)vertical bar Sigma(x is an element of Lambda L) u(t,x), where the field {u(t,x) : x is an element of Z(d)} is composed of solutions of the parabolic Anderson equation u (t,X) = 1 + kappa integral(t)(0) Delta u(s,x) ds + integral(t)(o) u(s,x) partial derivative B-x (S). The index set is a box in Z(d), namely Lambda(L) = {x is an element of Z(d) : vertical bar x vertical bar <= L} and L = L(t) is a nondecreasing function L : [0...
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作者：Birge, Lucien; Massart, Pascal
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：This paper is mainly devoted to a precise analysis of what kind of penalties should be used in order to perform model selection via the minimization of a penalized least-squares type criterion within some general Gaussian framework including the classical ones. As compared to our previous paper on this topic (Birge and Massart in J. Eur. Math. Soc. 3, 203-268 (2001)), more elaborate forms of the penalties are given which are shown to be, in some sense, optimal. We indeed provide more precise u...
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作者：Bobkov, Sergey G.; Goetze, Friedrich
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：Concentration properties and an asymptotic behaviour of distributions of normalized and self-normalized sums are studied in the randomized model where the observation times are selected from prescribed consecutive integer intervals.
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作者：Johansson, K.
作者单位：Royal Institute of Technology
摘要：The Tracy-Widom distribution that has been much studied in recent years can be thought of as an extreme value distribution. We discuss interpolation between the classical extreme value distribution exp(- exp(-x)), the Gumbel distribution, and the Tracy-Widom distribution. There is a family of determinantal processes whose edge behaviour interpolates between a Poisson process with density exp(-x) and the Airy kernel point process. This process can be obtained as a scaling limit of a grand canon...
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作者：Chistyakov, G. P.; Goetze, F.
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; University of Bielefeld
摘要：We extend the classical Darmois-Skitovich theorem to the case where the linear forms L-r1 = U1X1 +center dot center dot center dot+ UnXn and L-r2 = Un+1X1+center dot center dot center dot+U2nXn have random coefficients U-1,...,U-2n. Under minimal restrictions on the random coefficients we completely describe the distributions of the independent random variables X-1,...,X-n and U-1,...,U-2n such that the linear forms L-r1 and L-r2 are independent.
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作者：Gozlan, Nathael; Leonard, Christian
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Nanterre
摘要：New transportation cost inequalities are derived by means of elementary large deviation reasonings. Their dual characterization is proved; this provides an extension of a well-known result of S. Bobkov and F. Gotze. Their tensorization properties are investigated. Sufficient conditions (and necessary conditions too) for these inequalities are stated in terms of the integrability of the reference measure. Applying these results leads to new deviation results: concentration of measure and deviat...
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作者：Chatterjee, Sourav
作者单位：University of California System; University of California Berkeley
摘要：We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.
