Dear all,

I would like to announce the following talk that will be held on Tuesday, May 7th 2019, at 4:30 PM in Aula Dal Passo of the Department of Mathematics, University of Rome Tor Vergata.

Speaker: Jacques Franchi (I.R.M.A. Strasbourg)

Title: Small time equivalents for the density of a planar quadratic Langevin diffusion

Abstract: Exact small time equivalents for the density of the (heat kernel) semi-group, with a control of the error term, are obtained for a quadratic planar analogue of the Langevin diffusion, which is strictly hypoelliptic and non-Gaussian, hence of a different nature from the known Riemannian, sub-Riemannian and linear-Gaussian cases. Namely I consider the density  p_t  of  X_t := ( B_t , \int_0^t B_s^2 ds ), where  B_t  is real Brownian, and I obtain the asymptotic behaviours, as  t --> 0, of  p_t(0,(w,y)) and  p_t(0,(w,ty)), which both can be seen as natural extensions beyond the degenerate Langevin-Gaussian framework. The result for the scaled regime is the first such one in a non-Gaussian strictly hypoelliptic framework. The method is half-probabilistic half-analytic.

Kind regards,