Gradient estimates for positive harmonic functions by stochastic analysis

被引：13

作者：

Arnaudon, Marc

Driver, Bruce K.

Thalmaier, Anton

机构：

[1] Univ Luxembourg, Math Lab, L-1511 Luxembourg, Luxembourg

[2] Univ Poitiers, Dept Math, F-86962 Futuroscope, France

[3] Univ Calif San Diego, Dept Math 0112, La Jolla, CA 92093 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2007年 / 117卷 / 02期

基金：

美国国家科学基金会;

关键词：

harmonic function; curvature; gradient estimate; Harnack inequality;

D O I：

10.1016/j.spa.2006.07.002

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 Cheng-Yau type inequalities for positive harmonic functions on Riemannian manifolds by using methods of Stochastic Analysis. Rather than evaluating an exact Bismut formula for the differential of a harmonic function, our method relies on a Bismut type inequality which is derived by an elementary integration by parts argument from an underlying submartingale. It is the monotonicity inherited in this submartingale which allows us to establish the pointwise estimates. (C) 2006 Elsevier B.V. All rights reserved.

引用

页码：202 / 220

页数：19

共 13 条

[1]

[Anonymous], 1994, CAMBRIDGE MATH LIB

[2] Complete lifts of connections and stochastic Jacobi fields [J].