Derivatives of Feynman-Kac Semigroups

2016/11/14 by James Thompson, Thompson, James · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1611.04373

openalex publication_date 2016/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the logarithmic derivatives of the integral kernel. Stationary solutions are also considered. The arguments are based on local martingales, although the assumptions are purely geometric.

Citations

• Hessian formulas and estimates for parabolic Schrödinger operators

Cited by

• Hessian matrix estimates of heat-type equations via Bismut-Stroock Hessian formula

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