Displaying similar documents to “Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM”

Optional splitting formula in a progressively enlarged filtration

Shiqi Song (2014)

ESAIM: Probability and Statistics

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Let 𝔽 F be a filtration andbe a random time. Let 𝔾 G be the progressive enlargement of 𝔽 F with. We study the following formula, called the optional splitting formula: For any 𝔾 G-optional process, there exists an 𝔽 F-optional process and a function defined on [0∞] × (ℝ × ) being ℬ [ 0 , ∞ ] ⊗ 𝒪 ( 𝔽 ) ℬ[0,∞]⊗x1d4aa;(F) measurable, such that Y = Y ' 1 [ 0 , τ ) + Y ' ' ( τ ) 1 [ τ , ∞ ) . Y=Y′1[0,τ)+Y′′(τ)1[τ,∞). (This formula can also be formulated for multiple random times ...

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

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Let (Ω, ℱ , ( ℱ t ), ℙ ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to ℱ ∞ (the-algebra generated by ( ℱ t )) a coherent family of probability measures ( ℚ t ) indexed by , each of them being defined on ℱ t . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative...

A new H(div)-conforming p-interpolation operator in two dimensions

Alexei Bespalov, Norbert Heuer (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper we construct a new H(div)-conforming projection-based -interpolation operator that assumes only H() ∩ 𝐇 ˜ (div, )-regularity ( > 0) on the reference element (either triangle or square) . We show that this operator is stable with respect to polynomial degrees and satisfies the commuting diagram property. We also establish an estimate for the interpolation error in the norm of the space 𝐇 ˜ (div, ), which is closely related...

Necessary and sufficient condition for the existence of a Fréchet mean on the circle

Benjamin Charlier (2013)

ESAIM: Probability and Statistics

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Let ( 𝕊 1 , d 𝕊 1 S 1 , d S 1 ) be the unit circle in ℝ endowed with the arclength distance. We give a sufficient and necessary condition for a general probability measure to admit a well defined Fréchet mean on ( 𝕊 1 , d 𝕊 1 S 1 , d S 1 ). We derive a new sufficient condition of existence() with no restriction on the support of the measure. Then, we study the convergence of the empirical Fréchet mean to the Fréchet mean and we give an algorithm to compute it.

Some problems in automata theory which depend on the models of set theory

Olivier Finkel (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We prove that some fairly basic questions on automata reading infinite words depend on the models of the axiomatic system ZFC. It is known that there are only three possibilities for the cardinality of the complement of an -language L ( 𝒜 ) (x1d49c;) accepted by a Büchi 1-counter automaton 𝒜 x1d49c;. We prove the following surprising result: there exists a 1-counter Büchi automaton 𝒜 x1d49c; such that the cardinality of the complement L ( 𝒜 ) - (𝒜) of the -language...

Gamma-convergence results for phase-field approximations of the 2D-Euler Elastica Functional

Luca Mugnai (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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We establish some new results about the -limit, with respect to the -topology, of two different (but related) phase-field approximations { ℰ } , { ℰ ˜ } ℰ ε ε ,   x10ff65; ℰ ε ε of the so-called Euler’s Elastica Bending Energy for curves in the plane. In particular we characterize the-limit as  → 0 of ℰ, and show that in general the -limits of ℰand ℰ ˜ x10ff65; ℰ ε do not coincide on indicator functions of sets with non-smooth boundary. More precisely we show that the domain of the-limit...

Multi-Harnack smoothings of real plane branches

Pedro Daniel González Pérez, Jean-Jacques Risler (2010)

Annales scientifiques de l'École Normale Supérieure

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Let Δ ⊂ 𝐑 2 be an integral convex polygon. G. Mikhalkin introduced the notion of, a class of real algebraic curves, defined by polynomials supported on Δ and contained in the corresponding toric surface. He proved their existence, viamethod, and that the topological type of their real parts is unique (and determined by Δ ). This paper is concerned with the description of the analogous statement in the case of a smoothing of a real plane branch ( C , 0 ) . We introduce the class ofsmoothings of ( C , 0 ) by...

Exact simulation for solutions of one-dimensional Stochastic Differential Equations with discontinuous drift

Pierre Étoré, Miguel Martinez (2014)

ESAIM: Probability and Statistics

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In this note we propose an exact simulation algorithm for the solution of (1) d X t = d W t + b ¯ ( X t ) d t , X 0 = x , d X t = d W t + b̅ ( X t ) d t,   X 0 = x, where b ¯ b̅is a smooth real function except at point 0 where b ¯ ( 0 + ) ≠ b ¯ ( 0 - ) b̅(0 + ) ≠ b̅(0 −) . The main idea is to sample an exact skeleton of Xusing an algorithm deduced from the convergence of the solutions of the skew...

Estimate of the pressure when its gradient is the divergence of a measure. Applications

Marc Briane, Juan Casado-Díaz (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, a W - 1 , N ' estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on ℝ N , or on a regular bounded open set of  ℝ N . The proof is based partially on the Strauss inequality [Strauss, 23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [ 9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the divergence of a measure, and...

Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations

Antoine Gloria (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We introduce and analyze a numerical strategy to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. In particular, we consider the simplest case possible: An elliptic equation on the -dimensional lattice ℤ d with independent and identically distributed conductivities on the associated edges. Recent results by Otto and the author quantify the error made by approximating the homogenized coefficient by the averaged energy of a regularized corrector...

Scaling laws for non-euclidean plates and the W 2 , 2 isometric immersions of riemannian metrics

Marta Lewicka, Mohammad Reza Pakzad (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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Recall that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one seeks a deformation yielding the closest metric realization. We set up a variational formulation of this problem by introducing the non-Euclidean version of the nonlinear elasticity functional, and establish its -convergence under...

Exact null internal controllability for the heat equation on unbounded convex domains

Viorel Barbu (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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The liner parabolic equation y t - 1 2 𝔻 y + F · y = 1 → 0 u ∂y ∂t − 1 2   Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝ with smooth boundary is exactly null controllable on each finite interval if 𝒪is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of x1d4aa; . Here, : ℝ → ℝ is a bounded, -continuous function, and  = ∇, where is convex and coercive.

Expansions for the distribution of M-estimates with applications to the Multi-Tone problem

Christopher S. Withers, Saralees Nadarajah (2011)

ESAIM: Probability and Statistics

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We give a stochastic expansion for estimates θ ^ that minimise the arithmetic mean of (typically independent) random functions of a known parameter. Examples include least squares estimates, maximum likelihood estimates and more generally -estimates. This is used to obtain leading cumulant coefficients of θ ^ needed for the Edgeworth expansions for the distribution and density ) to magnitude (or to for the symmetric...

Compact convex sets of the plane and probability theory

Jean-François Marckert, David Renault (2014)

ESAIM: Probability and Statistics

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The Gauss−Minkowski correspondence in ℝ states the existence of a homeomorphism between the probability measures on [0,2] such that ∫ 0 2 π e i x d μ ( x ) = 0 ∫ 0 2 π e ix d μ ( x ) = 0 and the compact convex sets (CCS) of the plane with perimeter 1. In this article, we bring out explicit formulas relating the border of a CCS to its probability measure. As a consequence, we show that some natural operations on CCS – for example, the Minkowski sum – have natural translations in terms of probability measure operations,...

Limit theorems for stationary Markov processes with L2-spectral gap

Déborah Ferré, Loïc Hervé, James Ledoux (2012)

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

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Let ( X t , Y t ) t ∈ 𝕋 be a discrete or continuous-time Markov process with state space 𝕏 × ℝ d where 𝕏 is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. ( X t , Y t ) t ∈ 𝕋 is assumed to be a Markov additive process. In particular, this implies that the first component ( X t ) t ∈ 𝕋 is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process ( Y t ) t ∈ 𝕋 is shown...

A proof of Reidemeister-Singer’s theorem by Cerf’s methods

François Laudenbach (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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Heegaard splittings and Heegaard diagrams of a closed 3-manifold M are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on M . We make use in a very simple setting of techniques which Jean Cerf developed for solving a famous problem. In passing, we show how to cancel the supernumerary local extrema in a generic path of functions when dim M > 2 . The main tool that we introduce is an which could be useful elsewhere.

Constructive quantization: approximation by empirical measures

Steffen Dereich, Michael Scheutzow, Reik Schottstedt (2013)

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

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In this article, we study the approximation of a probability measure μ on ℝ d by its empirical measure μ ^ N interpreted as a random quantization. As error criterion we consider an averaged p th moment Wasserstein metric. In the case where 2 p l t ; d , we establish fine upper and lower bounds for the error, a. Moreover, we provide a universal estimate based on moments, a . In particular, we show that quantization by empirical measures is of optimal order under weak assumptions.

Face-to-face partition of 3D space with identical well-centered tetrahedra

Radim Hošek (2015)

Applications of Mathematics

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The motivation for this paper comes from physical problems defined on bounded smooth domains Ω in 3D. Numerical schemes for these problems are usually defined on some polyhedral domains Ω h and if there is some additional compactness result available, then the method may converge even if Ω h → Ω only in the sense of compacts. Hence, we use the idea of meshing the whole space and defining the approximative domains as a subset of this partition. Numerical schemes for which quantities are defined...

Curvature measures, normal cycles and asymptotic cones

Xiang Sun, Jean-Marie Morvan (2013)

Actes des rencontres du CIRM

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The purpose of this article is to give an overview of the theory of the and to show how to use it to define a on singular surfaces embedded in an (oriented) Euclidean space 𝔼 3 . In particular, we will introduce the notion of associated to a Borel subset of 𝔼 3 , generalizing the defined at each point of a smooth surface. For simplicity, we restrict our singular subsets to polyhedra of the 3 -dimensional Euclidean space 𝔼 3 . The coherence of the theory lies in a convergence theorem: If a...

A new perspective on some approximations used in neutron transport modeling

Hanuš, Milan

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In this contribution, we will use the (introduced in [1,2]) to derive a system of partial differential equations governing transport of neutrons within an interacting medium. This system forms an alternative to the well known P N approximation, which is based on the expansion of the directional dependence into tesseral spherical harmonics ([3,p.197]). In comparison with this latter set of equations, the Maxwell-Cartesian system posesses a much more regular structure, which may be used...