Derivative and divergence formulae for diffusion semigroups
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 shiftHarnack inequalities.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 DOI:
 10.48550/arXiv.1701.03625
 arXiv:
 arXiv:1701.03625
 Bibcode:
 2017arXiv170103625T
 Keywords:

 Mathematics  Probability