Christoph Baumgarten (2014)
ESAIM: Probability and Statistics
Similarity:
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 ,...,...
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...
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 = ∑ ...
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, ∞).
Rita Ferreira, Luísa M. Mascarenhas, Andrey Piatnitski (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
The paper deals with a Dirichlet spectral problem for an elliptic operator with -periodic coefficients in a 3D bounded domain of small thickness . We study the asymptotic behavior of the spectrum as and tend to zero. This asymptotic behavior depends crucially on whether and are of the same order ( ≈ ), or is much less than ( = < 1), or is much greater than ( = > 1). We consider all three cases. ...
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 ( ...
Xavier Gendre (2014)
ESAIM: Probability and Statistics
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Let ∈ ℝ be a random vector with mean and covariance matrix where is some known × -matrix. We construct a statistical procedure to estimate as well as under moment condition on or Gaussian hypothesis. Both cases are developed for known or unknown . Our approach is free from any prior assumption on and is based on non-asymptotic model selection methods....
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⌈...
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...
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...
Rita Ferreira, Luísa M. Mascarenhas, Andrey Piatnitski (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
The paper deals with a Dirichlet spectral problem for an elliptic operator with -periodic coefficients in a 3D bounded domain of small thickness . We study the asymptotic behavior of the spectrum as and tend to zero. This asymptotic behavior depends crucially on whether and are of the same order ( ≈ ), or is much less than ( = < 1), or is much greater than ...
Tze Leng Lai, Qi-Man Shao, Qiying Wang (2011)
ESAIM: Probability and Statistics
Similarity:
Let be a Studentized U-statistic. It is proved that a Cramér type moderate deviation ( ≥ )/(1 − Φ()) → 1 holds uniformly in ∈ [0, ( )) when the kernel satisfies some regular conditions.