Random obstacle problems, and integration by parts formulae for the laws of Bessel bridges
schedule le lundi 28 mai 2018 de 17h00 à 18h00
Organisé par : C. Cosco, S. Coste, L. Marêché, P. Melotti, N. Meyer
Intervenant : Henri Elad-Altman (Laboratoire de Probabilités, Statistique et Modélisation)
Lieu : Sophie Germain, salle 1016
Sujet : Random obstacle problems, and integration by parts formulae for the laws of Bessel bridges
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.