Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces (Q2174998)

The authors consider diffusions on Riemannian foliations equipped with a sub-Riemannian structure and \(\operatorname{RCD}^{\ast}\left( K, N \right)\) spaces. The main results include moment estimates, exponential integrability, concentration inequalities and exit times estimates for such diffusions. In addition to stochastic analysis tools such as Itô's formula,the authors rely on recent results on a Laplacian comparison in such degenerate settings where standard Riemannian techniques are not available. As an application, pointwise eigenfunction estimates of Schrödinger's operators are given.