Title: Degenerate diffusions and their limiting behaviors

Date: 12/01/2017

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

We discuss degenerate hypoelliptic diffusion processes and their limiting behaviors in both large time and small time. By studying the limiting behavior of a diffusion on a sub-Riemannian manifold, we are able to extract the underlying geometric information. Questions related to large time behavior such as stochastic completeness and convergence to equilibrium are closely related to global geometric bounds including Ricci curvature lower bound. Small time behavior of its transition density falls into the regime of large deviation estimate, which reveals the information of sub-Riemannian distance and has nice application in heat content problems. In this talk we will also discuss small time behavior of strict-degenerate diffusions (weak Hormander’s type). We obtain a graded large deviation principle for diffusions on a nilpotent Lie group. Parts of this talk are based on joint work with Fabrice Baudoin, Gerard Ben Arous, and Jeremy Tyson.