Andriy Yurachkivsky (2011)
ESAIM: Probability and Statistics
Similarity:
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...
Andrew Lorent (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
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...
Fábio Júlio Valentim (2012)
Annales de l'I.H.P. Probabilités et statistiques
Similarity:
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 = ∑ ...
Marc Arnaudon, Laurent Miclo (2014)
ESAIM: Probability and Statistics
Similarity:
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 ( ...
Nastasiya F. Grinberg (2013)
ESAIM: Probability and Statistics
Similarity:
In this note we prove that the local martingale part of a convex function of a -dimensional semimartingale = + can be written in terms of an Itô stochastic integral ∫()d, where () is some particular measurable choice of subgradient ∇ f ( x ) of at , and is the martingale part of . This result was first proved by Bouleau in [N. Bouleau, 292 (1981) 87–90]. Here we present a new treatment of the problem. We first prove the result for x10ff65; X = X + ϵB , > 0, where is...
Hedy Attouch, Paul-Émile Maingé (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
In the setting of a real Hilbert space , we investigate the asymptotic behavior, as time goes to infinity, of trajectories of second-order evolution equations () + () + (()) + (()) = 0, where is the gradient operator of a convex differentiable potential function : ,: is a maximal monotone operator which is assumed to be-cocoercive, and > 0 is a damping parameter. Potential and non-potential effects are associated...
Iosif Pinelis (2012)
ESAIM: Probability and Statistics
Similarity:
If a probability density (x) (x ∈ ℝ) is bounded and := ∫e (x)dx < ∞ for some linear functional u and all ∈ (01), then, for each ∈ (01) and all large enough , the -fold convolution of the -tilted density ˜pt := e (x)/ is bounded. This is a corollary of a general, “non-i.i.d.” result, which is also shown to enjoy a certain optimality property. Such results and their corollaries stated in terms of the absolute integrability of the corresponding characteristic...
Gaëlle Chagny (2013)
ESAIM: Probability and Statistics
Similarity:
This paper deals with the problem of estimating a regression function , in a random design framework. We build and study two adaptive estimators based on model selection, applied with warped bases. We start with a collection of finite dimensional linear spaces, spanned by orthonormal bases. Instead of expanding directly the target function on these bases, we rather consider the expansion of = ∘ , where is the cumulative distribution function of the design, following...
Jérôme Dedecker, Adeline Samson, Marie-Luce Taupin (2014)
ESAIM: Probability and Statistics
Similarity:
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...
Sara Brofferio, Dariusz Buraczewski, Ewa Damek (2012)
Annales de l'I.H.P. Probabilités et statistiques
Similarity:
We consider the autoregressive model on ℝ defined by the stochastic recursion = −1 + , where {( , )} are i.i.d. random variables valued in ℝ× ℝ+. The critical case, when , was studied by Babillot, Bougerol and Elie, who proved that there exists a unique invariant Radon measure for the Markov chain { }. In the present paper we prove that the weak limit of properly...
Luís Balsa Bicho, António Ornelas (2014)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
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...
Jean-François Couchouron (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
This paper deals with feedback stabilization of second order equations of the form + + = 0, ∈ [0, +∞[, where is a densely defined positive selfadjoint linear operator on a real Hilbert space with compact inverse and is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control = ⟨, ...
Pierre Bousquet (2013)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We consider a nonlinear elliptic equation of the form div [(∇)] + [] = 0 on a domain Ω, subject to a Dirichlet boundary condition tr = . We do not assume that the higher order term satisfies growth conditions from above. We prove the existence of continuous solutions either when Ω is convex and satisfies a one-sided bounded slope condition, or when is radial: a ( ξ ) = l ( | ξ | ) | ξ | ξ for some increasing:ℝ → ℝ
Jean-François Couchouron (2011)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
This paper deals with feedback stabilization of second order equations of
the form
Gengsheng Wang, Yashan Xu (2014)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
This paper studies the periodic feedback stabilization of the controlled linear time-periodic ordinary differential equation: () = ()() + ()(), ≥ 0, where [(·)(·)] is a -periodic pair, , (·) ∈ (ℝ; ℝ) and (·) ∈ (ℝ; ℝ) satisfy respectively ( + ) = () for a.e. ≥ 0 and ( + ) = () for a.e. ≥ 0. Two periodic stablization criteria for a -period pair [(·)(·)] are established. One is an analytic criterion which is related to the transformation over time associated...
Jean Brossard, Christophe Leuridan (2012)
Annales de l'I.H.P. Probabilités et statistiques
Similarity:
Let be a measurable transformation of a probability space , preserving the measure. Let be a random variable with law . Call (⋅, ⋅) a regular version of the conditional law of given (). Fix . We first prove that if is reachable from -almost every point for a Markov chain of kernel , then the -orbit of -almost every point visits . We then apply this result to the Lévy transform, which transforms the Brownian motion into the Brownian motion || − , where is the local time at 0...
József Balogh, Béla Bollobás (2010)
RAIRO - Theoretical Informatics and Applications
Similarity:
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⌈...
Denis Belomestny (2010)
ESAIM: Probability and Statistics
Similarity:
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...
Arturo Carpi, Aldo de Luca (2010)
RAIRO - Theoretical Informatics and Applications
Similarity:
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 ...