Translator Disclaimer
March 2019 Derivative and divergence formulae for diffusion semigroups
Anton Thalmaier, James Thompson
Ann. Probab. 47(2): 743-773 (March 2019). DOI: 10.1214/18-AOP1269

Abstract

For a semigroup $P_{t}$ generated by an elliptic operator on a smooth manifold $M$, 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-Harnack inequalities.

Citation

Download Citation

Anton Thalmaier. James Thompson. "Derivative and divergence formulae for diffusion semigroups." Ann. Probab. 47 (2) 743 - 773, March 2019. https://doi.org/10.1214/18-AOP1269

Information

Received: 1 January 2017; Revised: 1 February 2018; Published: March 2019
First available in Project Euclid: 26 February 2019

zbMATH: 07053555
MathSciNet: MR3916933
Digital Object Identifier: 10.1214/18-AOP1269

Subjects:
Primary: 58J65, 60J60
Secondary: 53C21

Rights: Copyright © 2019 Institute of Mathematical Statistics

JOURNAL ARTICLE
31 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 2 • March 2019
Back to Top