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作者：Cattiaux, P.; Gentil, I.; Guillin, A.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite Paris Nanterre; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincare inequalities, general Beckner inequalities, etc.). We also discuss the quantitative behaviour of relative entropy along a symmetric diffusion semi-group. In particular, we exhibit an example where Poincare inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.
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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：van der Hofstad, Remco; den Hollander, Frank; Slade, Gordon
作者单位：Leiden University; Leiden University - Excl LUMC; Eindhoven University of Technology; University of British Columbia
摘要：We consider critical spread-out oriented percolation above 4 + 1 dimensions. Our main result is that the extinction probability at time n (i.e., the probability for the origin to be connected to the hyperplane at time n but not to the hyperplane at time n + 1) decays like 1/Bn-2 as n -> infinity, where B is a finite positive constant. This in turn implies that the survival probability at time n (i.e., the probability that the origin is connected to the hyperplane at time n) decays like 1/Bn-2 ...
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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：Pinelis, Iosif
作者单位：Michigan Technological University
摘要：Let BS1,..., BSn be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter p is an element of (0,1). Let m(*)(p) := (1 + p + 2p(2))/(2 root p - p(2) + 4p(2)) if 0 < p <= 1/2 and m(*)(p) := 1 if 1/2 <= p < 1. Let m >= m(*)(p). Let f be such a function that f and f '' are nondecreasing and convex. Then it is proved that for all nonnegative numbers c(1),..., c(n) one has the inequality Ef(c(1)BS(1) + center dot center dot center dot...
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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：Bass, Richard F.; Lavrentiev, Alexander
作者单位：University of Connecticut; University of Wisconsin System
摘要：We consider the degenerate elliptic operator acting on C-b(2) functions on [0,infinity) (d): [GRAPHIC] where the a(i) are continuous functions that are bounded above and below by positive constants, the bi are bounded and measurable, and the alpha(i) is an element of (0, 1). We impose Neumann boundary conditions on the boundary of [0,infinity)(d). There will not be uniqueness for the submartingale problem corresponding to L. If we consider, however, only those solutions to the submartingale pr...
