Sub-Riemannian geometries and hypoelliptic diffusion processes |
Karen Habermann, University of Warwick |
Donnerstag, 2024-06-13 14:00Uhr |
|
I will start with an overview on sub-Riemannian geometries, where motion is only possible along certain admissible trajectories, and hypoelliptic diffusion processes, which due to underlying constraints spread in different directions at different orders. Subsequently, I will present two projects where the analysis of stochastic processes on constrained systems has proven to be fruitful. Firstly, I will discuss how a stochastic process introduced jointly with Barilari, Boscain and Cannarsa on surfaces in three-dimensional contact sub-Riemannian manifolds can be used to classify singular points arising in that setting. Secondly, I will show how the study of a standard one-dimensional Brownian motion conditioned to have vanishing iterated time integrals of all orders, which can be rephrased as studying projected hypoelliptic diffusion loops, has led to a novel polynomial approximation for Brownian motion.. |