On the Differentiation of Heat Semigroups and Poisson Integrals
by Anton Thalmaier

We give a version of integration by parts on the level of local martingales; combined with the optional sampling theorem, this method allows us to obtain differentiation formulae for Poisson integrals in the same way as for heat semigroups involving boundary conditions. In particular, our results yield Bismut type representations for the logarithmic derivative of the Poisson kernel on regular domains in Riemannian manifolds corresponding to elliptic PDOs of Hörmander type. Such formulae provide a direct approach to gradient estimates for harmonic functions on Riemannian manifolds.

Stochastics and Stochastics Reports 61 (1997) 297-321

The paper is available here:

Anton Thalmaier <anton.thalmaier@uni.lu>

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