Andriy Yurachkivsky (2011)
ESAIM: Probability and Statistics
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Let, for each ∈ , (, ۔) be a random measure on the Borel -algebra in ℝ such that E(, ℝ) < ∞ for all and let (, ۔) be its characteristic function. We call the function ( ,…, ; ,…, ) = of arguments ∈ ℕ, , … ∈ , , ∈ ℝ the of the measure-valued random function (MVRF) (۔, ۔). A general limit theorem for MVRF's in terms of covaristics is proved and...
Fábio Júlio Valentim (2012)
Annales de l'I.H.P. Probabilités et statistiques
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Fix a polynomial of the form () = + ∑2≤≤ =1 with (1) gt; 0. We prove that the evolution, on the diffusive scale, of the empirical density of exclusion processes on , with conductances given by special class of functions, is described by the unique weak solution of the non-linear parabolic partial differential equation = ∑ ...
Andrew Lorent (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain ⊂ ℝthe functional is I ϵ ( u ) = 1 2 ∫ Ω ϵ -1 1 − Du 2 2 + ϵ D 2 u 2 d z wherebelongs to the subset of functions in W02,2(Ω) whose gradient (in the sense of trace) satisfies()· = 1 where is the inward pointing unit normal to at . In [1...
Marc Arnaudon, Laurent Miclo (2014)
ESAIM: Probability and Statistics
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Let be a complete Riemannian manifold, ∈ ℕ and ≥ 1. We prove that almost everywhere on = ( ,, ) ∈ for Lebesgue measure in , the measure μ ( x ) = 1 N ∑ k = 1 N δ x k has a unique–mean (). As a consequence, if = ( ,, ) is a -valued random variable with absolutely continuous law, then almost surely (()) has a unique –mean. In particular if ( ...
Luís Balsa Bicho, António Ornelas (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove of vector minimizers () = (||) to multiple integrals ∫ ((), |()|) on a ⊂ ℝ, among the Sobolev functions (·) in + (, ℝ), using a : ℝ×ℝ → [0,∞] with (·) and . Besides such basic hypotheses, (·,·) is assumed to satisfy also...
Marie Theret (2014)
ESAIM: Probability and Statistics
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We consider the standard first passage percolation model in ℤ for ≥ 2 and we study the maximal flow from the upper half part to the lower half part (respectively from the top to the bottom) of a cylinder whose basis is a hyperrectangle of sidelength proportional to and whose height is () for a certain height function . We denote this maximal flow by (respectively ). We emphasize the fact that the cylinder may be tilted. We look at the probability that...
Jérôme Dedecker, Adeline Samson, Marie-Luce Taupin (2014)
ESAIM: Probability and Statistics
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Consider an autoregressive model with measurement error: we observe = + , where the unobserved is a stationary solution of the autoregressive equation = ( ) + . The regression function is known up to a finite dimensional parameter to be estimated. The distributions of and are unknown and...
Christoph Baumgarten (2014)
ESAIM: Probability and Statistics
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Given an autoregressive process of order ( = + ··· + + where the random variables , ,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time (survival or persistence probability). Depending on the coefficients ,...,...
Elena Di Bernardino, Thomas Laloë, Véronique Maume-Deschamps, Clémentine Prieur (2013)
ESAIM: Probability and Statistics
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This paper deals with the problem of estimating the level sets () = {() ≥ }, with ∈ (0,1), of an unknown distribution function on ℝ . A plug-in approach is followed. That is, given a consistent estimator of , we estimate () by () = { () ≥ }. In our setting, non-compactness property is required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric...
József Balogh, Béla Bollobás (2010)
RAIRO - Theoretical Informatics and Applications
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Let be a hereditary property of words, , an infinite class of finite words such that every subword (block) of a word belonging to is also in . Extending the classical Morse-Hedlund theorem, we show that either contains at least words of length for every or, for some , it contains at most words of length for every . More importantly, we prove the following quantitative extension of this result: if has words of length then, for every , it contains at most ⌈( + 1)/2⌉⌈( + 1)/2⌈...
Sandrine Péché (2012)
Annales de l'I.H.P. Probabilités et statistiques
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We consider complex sample covariance matrices = (1/)* where is a × random matrix with i.i.d. entries , 1 ≤ ≤ , 1 ≤ ≤ , with distribution . Under some regularity and decay assumptions on , we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where → ∞ and lim→∞ / = for any real number ∈ (0, ∞).
Serge Dubuc, Issa Kagabo, Patrice Marcotte (2010)
RAIRO - Operations Research
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Let and be two compact spaces endowed with respective measures and satisfying the condition . Let be a continuous function on the product space . The mass transfer problem consists in determining a measure on whose marginals coincide with and , and such that the total cost be minimized. We first show that if the cost function is decomposable, i.e., can be represented as the sum of two continuous functions defined on and , respectively, then every feasible measure is optimal....
Arturo Carpi, Aldo de Luca (2010)
RAIRO - Theoretical Informatics and Applications
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For any finite word on a finite alphabet, we consider the basic parameters and of defined as follows: is the minimal natural number for which has no right special factor of length and is the minimal natural number for which has no repeated suffix of length . In this paper we study the distributions of these parameters, here called characteristic parameters, among the words ...
Denis Belomestny (2010)
ESAIM: Probability and Statistics
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Let () be independent identically distributed bivariate vectors and , are two linear forms with positive coefficients. We study two problems: under what conditions does the equidistribution of and imply the same property for and , and under what conditions does the independence of and entail independence of and ? Some analytical sufficient conditions...