Strong regularization by noise for a class of kinetic SDEs

This talk will focus on recent results on pathwise uniqueness for degenerate stochastic differential equations with irregular coefficients. This phenomenon is known as “regularization by noise”: an ill-posed differential equation is made well-posed adding a random term. We will present strong well-posedness for a class of kinetic-type SDEs driven by symmetric stable processes with drift coefficients that are Hölder continuous in the space variables and measurable in time. In particular, we study the case with autonomous diffusion and we partially recover the thresholds for the Hölder regularity that are optimal for weak uniqueness. Two different strategies and results are presented for the one-dimensional and the multi-dimensional cases.

This presentation is based on a joint work with Stéphane Menozzi (Université d'Évry Val d'Essonne) and Stefano Pagliarani (Università di Bologna).