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Diffusions infini-dimensionnelles et champs de Gibbs sur l'espace
des trajectoires continues

Abstract : The Gibbsian nature of infinite-dimensional gradient diffusions is here analyzed. They modelize interacting Brownian particles systems . Representing the solutions of such systems by point processes on pathspace, we prove the equivalence between to be the law of a gradient diffusion and to be a Gibbs field on continuous pathspace for a particular dynamical local Hamiltonian. More generally, we prove that every regular Gibbs field on pathspace may be represented by an infinite-dimensional diffusion for which we compute the drift. We give many applications o these results ; for example, a time reversal formula for the gradient diffusions is proved and so, we study reversibility and stationarity for such diffusions.
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Contributor : David Dereudre <>
Submitted on : Monday, February 10, 2003 - 5:16:34 PM
Last modification on : Friday, January 10, 2020 - 3:42:10 PM
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David Dereudre. Diffusions infini-dimensionnelles et champs de Gibbs sur l'espace
des trajectoires continues. Mathématiques [math]. Ecole Polytechnique X, 2002. Français. ⟨tel-00002373⟩

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