Displaying similar documents to “Large deviations, central limit theorems and Lp convergence for Young measures and stochastic homogenizations”

A Young measures approach to quasistatic evolution for a class of material models with nonconvex elastic energies

Alice Fiaschi (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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Rate-independent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution...

Asymptotic behaviour of stochastic quasi dissipative systems

Giuseppe Da Prato (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.

On a stochastic SIR model

Elisabetta Tornatore, Stefania Maria Buccellato (2007)

Applicationes Mathematicae

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We consider a stochastic SIR system and we prove the existence, uniqueness and positivity of solution. Moreover the existence of an invariant measure under a suitable condition on the coefficients is studied.

Recent advances in ambit stochastics with a view towards tempo-spatial stochastic volatility/intermittency

Ole E. Barndorff-Nielsen, Fred Espen Benth, Almut E. D. Veraart (2015)

Banach Center Publications

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Ambit stochastics is the name for the theory and applications of ambit fields and ambit processes and constitutes a new research area in stochastics for tempo-spatial phenomena. This paper gives an overview of the main findings in ambit stochastics up to date and establishes new results on general properties of ambit fields. Moreover, it develops the concept of tempo-spatial stochastic volatility/intermittency within ambit fields. Various types of volatility modulation ranging from stochastic...

A note on weak solutions to stochastic differential equations

Martin Ondreját, Jan Seidler (2018)

Kybernetika

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We revisit the proof of existence of weak solutions of stochastic differential equations with continuous coeficients. In standard proofs, the coefficients are approximated by more regular ones and it is necessary to prove that: i) the laws of solutions of approximating equations form a tight set of measures on the paths space, ii) its cluster points are laws of solutions of the limit equation. We aim at showing that both steps may be done in a particularly simple and elementary manner. ...

Homogenization of periodic nonconvex integral functionals in terms of Young measures

Omar Anza Hafsa, Jean-Philippe Mandallena, Gérard Michaille (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.