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2020 Radial processes for sub-Riemannian Brownian motions and applications
Fabrice Baudoin, Erlend Grong, Kazumasa Kuwada, Robert Neel, Anton Thalmaier
Electron. J. Probab. 25: 1-17 (2020). DOI: 10.1214/20-EJP501

Abstract

We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô’s formula is proved for the radial processes associated to Riemannian distances approximating the Riemannian one. We deduce very general stochastic completeness criteria for the sub-Riemannian Brownian motion. In the context of Sasakian foliations and H-type groups, one can push the analysis further, and taking advantage of the recently proved sub-Laplacian comparison theorems one can compare the radial processes for the sub-Riemannian distance to one-dimensional model diffusions. As a geometric application, we prove Cheng’s type estimates for the Dirichlet eigenvalues of the sub-Riemannian metric balls, a result which seems to be new even in the Heisenberg group.

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Fabrice Baudoin. Erlend Grong. Kazumasa Kuwada. Robert Neel. Anton Thalmaier. "Radial processes for sub-Riemannian Brownian motions and applications." Electron. J. Probab. 25 1 - 17, 2020. https://doi.org/10.1214/20-EJP501

Information

Received: 7 February 2020; Accepted: 26 July 2020; Published: 2020
First available in Project Euclid: 13 August 2020

zbMATH: 07252729
MathSciNet: MR4136477
Digital Object Identifier: 10.1214/20-EJP501

Subjects:
Primary: 35H20, 53C17, 58J65

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