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Theses

INEGALITES LOG-SOBOLEV POUR LA LOI D'UNE DIFFUSION
ET GRANDES DEVIATIONS POUR DES EDP STOCHASTIQUES

Abstract : This thesis is devoted to the study of the ergodic behavior of certain dynamical systems.

In the first part, we establish the logarithmic Sobolev inequality for the Brownian motion with drift, and more generally for elliptic diffusions, on the path space equipped with a L2 metric. This inequality provides us interesting concentration properties for the large time behavior of certains additive functionals.

In the second part, one specifies the ergodic behavior of the stochastic Burgers and Navier-Stokes equations by giving a large deviation principle for empirical measure for large time.
It describes the exponential convergence to the unique equilibrium state, when the random force is sufficiently non-degenerate.
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https://tel.archives-ouvertes.fr/tel-00120651
Contributor : Mathieu Gourcy <>
Submitted on : Saturday, February 10, 2007 - 11:45:53 AM
Last modification on : Thursday, February 25, 2021 - 10:34:02 AM
Long-term archiving on: : Thursday, September 23, 2010 - 4:02:12 PM

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  • HAL Id : tel-00120651, version 3

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Mathieu Gourcy. INEGALITES LOG-SOBOLEV POUR LA LOI D'UNE DIFFUSION
ET GRANDES DEVIATIONS POUR DES EDP STOCHASTIQUES. Mathématiques [math]. Université Blaise Pascal - Clermont-Ferrand II, 2006. Français. ⟨tel-00120651v3⟩

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