## Séminaire Orléans

**Random obstacle problems, and integration by parts formulae for the laws of Bessel bridges**

Henri Elad Altman (UPMC)

Thursday 31 May 2018 14:00 - Orléans - Salle de Séminaire

**Résumé :**

In the early 2000s, Lorenzo Zambotti introduced a family of stochastic PDEs parametrized by a real number d larger or equal to 3. These equations model the random evolution of a continuous interface over a repulsive obstacle, and the parameter d gives the intensity of the repulsion. Moreover, their unique invariant measure corresponds to the law of a d-dimensional Bessel bridge. A long-standing open problem is to extend such results to d smaller than 3. In my talk, I will introduce these stochastic PDEs. I will also discuss conjectures for the dynamics associated with a parameter d smaller than 3, based on recently obtained integration by parts formulae for the laws of Bessel bridges. The particularly interesting case d = 1, which would correspond to an SPDE with the reflecting Brownian bridge as invariant measure, will be mentioned.

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