Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces
by Anton Thalmaier and James Thompson
Abstract
In this article we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions in two settings each beyond the scope of Riemannian geometry. Firstly, we consider sub-Riemannian limits of Riemannian foliations. Secondly, we consider the non-smooth setting of RCD*(K,N) spaces. In each case the necessary ingredients are an Itô formula and a comparison theorem for the Laplacian, for which we refer to the recent literature. As an application, we derive pointwise Carmona-type estimates on eigenfunctions of Schrödinger operators.
Bernoulli 26 (2020), no. 3, 2202-2225
https://dx.doi.org/10.3150/19-BEJ1190
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