Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds
by Qin-Qian Chen, Li-Juan Cheng and Anton Thalmaier
Abstract
In this article, we develop a martingale approach to localized Bismut-type Hessian formulas for heat
semigroups on Riemannian manifolds. Our approach extends the Hessian formulas established by Stroock (1996)
and removes in particular the compact manifold restriction. To demonstrate the potential of these formulas, we give
as application explicit quantitative local estimates for the Hessian of the heat semigroup, as well as for harmonic
functions on regular domains in Riemannian manifolds.
Stochastics and Partial Differential Equations 11 (2023), no. 2, 685-713
https://doi.org/10.1007/s40072-022-00241-1
The preprint version is available here:
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