Exponential integrability and exit times of diffusions on sub-Riemannian\n and metric measure spaces

2019/06/06 by Anton Thalmaier, James Thompson, Thalmaier, Anton +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1906.02661

openalex publication_date 2019/06/06 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

In this article we derive moment estimates, exponential integrability,\nconcentration inequalities and exit times estimates for canonical diffusions in\ntwo settings each beyond the scope of Riemannian geometry. Firstly, we consider\nsub-Riemannian limits of Riemannian foliations. Secondly, we consider the\nnon-smooth setting of \RCD^*(K,N) spaces. In each case the necessary\ningredients are an It ^o formula and a comparison theorem for the Laplacian,\nfor which we refer to the recent literature. As an application, we derive\npointwise Carmona-type estimates on eigenfunctions of Schr "odinger\noperators.\n

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• Sub-Laplacian comparison theorems on Riemannian foliations with minimal leaves and applications

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