STOCHASTIC ANALYSIS ON SUB-RIEMANNIAN MANIFOLDS WITH TRANSVERSE SYMMETRIES

被引：9

作者：

Baudoin, Fabrice ^{[1
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47906 USA

来源：

ANNALS OF PROBABILITY | 2017年 / 45卷 / 01期

基金：

美国国家科学基金会;

关键词：

Sample; Brownian motion; sub-Riemannian manifold; Bochner-Weitzenbock formula; CURVATURE-DIMENSION INEQUALITY; HYPOELLIPTIC HEAT-KERNEL; HEISENBERG-GROUP; OPERATORS; GRADIENT; GEOMETRY; BUNDLES;

D O I：

10.1214/14-AOP964

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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-Weitzenbock 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

引用

页码：56 / 81

页数：26

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