Limit theorems for measure-valued processes of the level-exceedance type

Andriy Yurachkivsky

Displaying similar documents to “Limit theorems for measure-valued processes of the level-exceedance type”

A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity

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 $I_{} (u) = \frac{1}{2} \int_{Ω}^{- 1} {| 1 - | D u |}^{2} |^{2} + {| D^{2} u |}^{2} d z$ 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 $W_{0}^{2, 2} (Ω)$ W02,2(Ω) whose gradient (in the sense of trace) satisfies()· = 1 where is the inward pointing unit normal to at . In [1...

Hydrodynamic limit of a d-dimensional exclusion process with conductances

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 $𝕋^{d}$ , with conductances given by special class of functions, is described by the unique weak solution of the non-linear parabolic partial differential equation = ∑ ...

Means in complete manifolds: uniqueness and approximation

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 $μ (x) = N \sum_{k = 1}^{N} x_{k}$ 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 ( ...

On the invariant measure of the random difference equation Xn = AnXn−1 + Bn in the critical case

Sara Brofferio, Dariusz Buraczewski, Ewa Damek (2012)

Annales de l'I.H.P. Probabilités et statistiques

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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 $𝔼 [log A_{1}] = 0$ , 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...

Semimartingale decomposition of convex functions of continuous semimartingales by brownian perturbation

Nastasiya F. Grinberg (2013)

ESAIM: Probability and Statistics

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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 $\tilde{X} = X + ϵ B$ x10ff65; X = X + ϵB , > 0, where is...

Estimation in autoregressive model with measurement error

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...

Exponential deficiency of convolutions of densities

Iosif Pinelis (2012)

ESAIM: Probability and Statistics

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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 ${\tilde{p}}_{t}$ ˜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...

Pointwise constrained radially increasing minimizers in the quasi-scalar calculus of variations

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...

Hereditary properties of words

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⌈...

Penalization versus Goldenshluger − Lepski strategies in warped bases regression

Gaëlle Chagny (2013)

ESAIM: Probability and Statistics

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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...

Universality in the bulk of the spectrum for complex sample covariance matrices

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, ∞).

Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory

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...

Trivial Cases for the Kantorovitch Problem

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....

Upper large deviations for maximal flows through a tilted cylinder

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...

Minimising convex combinations of low eigenvalues

Mette Iversen, Dario Mazzoleni (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the variational problem inf{ () + () + (1 − − ) () | Ω open in ℝ, || ≤ 1}, for ∈ [0, 1], + ≤ 1, where () is the th eigenvalue of the Dirichlet Laplacian acting in () and || is the Lebesgue measure of . We investigate for which values of every minimiser is connected.

Periodic stabilization for linear time-periodic ordinary differential equations

Gengsheng Wang, Yashan Xu (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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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...