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January 2017 Stochastic analysis on sub-Riemannian manifolds with transverse symmetries
Fabrice Baudoin
Ann. Probab. 45(1): 56-81 (January 2017). DOI: 10.1214/14-AOP964


We prove a geometrically meaningful stochastic representation of the derivative of the heat semigroup on sub-Riemannian manifolds with tranverse symmetries. This representation is obtained from the study of Bochner–Weitzenböck type formulas for sub-Laplacians on 1-forms. As a consequence, we prove new hypoelliptic heat semigroup gradient bounds under natural global geometric conditions. The results are new even in the case of the Heisenberg group which is the simplest example of a sub-Riemannian manifold with transverse symmetries.


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Fabrice Baudoin. "Stochastic analysis on sub-Riemannian manifolds with transverse symmetries." Ann. Probab. 45 (1) 56 - 81, January 2017.


Received: 1 February 2014; Revised: 1 June 2014; Published: January 2017
First available in Project Euclid: 26 January 2017

zbMATH: 06696265
MathSciNet: MR3601645
Digital Object Identifier: 10.1214/14-AOP964

Primary: 53C17 , 58J65
Secondary: 60J60

Keywords: Bochner–Weitzenböck formula , Brownian motion , Sample , sub-Riemannian manifold

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 1 • January 2017
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