DERIVATIVE AND DIVERGENCE FORMULAE FOR DIFFUSION SEMIGROUPS

• 成果类型: Article
• 署名作者: Thalmaier, Anton; Thompson, James
• 署名单位: University of Luxembourg
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1269
• 发表日期: 2019
• 页码: 743-773
• 关键词: bismut type formulas

摘要

For a semigroup P-t generated by an elliptic operator on a smooth mani-fold M, we use straightforward martingale arguments to derive probabilistic formulae for P-t (V(f)), not involving derivatives of f, where V is a vector field on M. For nonsymmetric generators, such formulae correspond to the derivative of the heat kernel in the forward variable. As an application, these formulae can be used to derive various shift-Hamack inequalities.