Displaying similar documents to “A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies”

Large deviations, central limit theorems and L convergence for Young measures and stochastic homogenizations

Julien Michel, Didier Piau (2010)

ESAIM: Probability and Statistics

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We study the stochastic homogenization processes considered by Baldi (1988) and by Facchinetti and Russo (1983). We precise the speed of convergence towards the homogenized state by proving the following results: (i) a large deviations principle holds for the Young measures; if the Young measures are evaluated on a given function, then (ii) the speed of convergence is bounded in every L norm by an explicit rate and (iii) central limit theorems hold. In dimension 1, we apply these...

Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach

Filippo Cagnetti, Rodica Toader (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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A new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [G. Dal Maso and C. Zanini, 137 (2007) 253–279] is recovered. In this case, the convergence of the discrete time approximations is improved.

Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit

Samuel Herrmann, Julian Tugaut (2012)

ESAIM: Probability and Statistics

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In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there exists a unique symmetric limit measure associated to the set...

Conditional distributions, exchangeable particle systems, and stochastic partial differential equations

Dan Crisan, Thomas G. Kurtz, Yoonjung Lee (2014)

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

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Stochastic partial differential equations (SPDEs) whose solutions are probability-measure-valued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing traders. Each trader’s valuations of the assets are given by the solution of a stochastic differential...

On the order equivalence relation of binary association measures

Mariusz Paradowski (2015)

International Journal of Applied Mathematics and Computer Science

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Over a century of research has resulted in a set of more than a hundred binary association measures. Many of them share similar properties. An overview of binary association measures is presented, focused on their order equivalences. Association measures are grouped according to their relations. Transformations between these measures are shown, both formally and visually. A generalization coefficient is proposed, based on joint probability and marginal probabilities. Combining association...

Elementary examples of Loewner chains generated by densities

Alan Sola (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We study explicit examples of Loewner chains generated by absolutely continuous driving measures, and discuss how properties of driving measures are reflected in the shapes of the growing Loewner hulls.